Question 1

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
-In one county, the conviction rate for speeding is 85%. Estimate the probability that of the next 100 speeding summonses issued, there will be at least 90 convictions.

Accepted Answer

The answer of Estimate the indicated probability by using the...

Question 2

For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation.
-$n = 15 \text { and } p = 0.2$

Accepted Answer

The normal approximation to the binomial distribution is suitable when both np and n(1-p) are greater than or equal to 5. Here, np = 15 * 0.2 = 3 and n(1-p) = 15 * 0.8 = 12. Since np is less than 5, the normal approximation is not suitable.

Question 3

The systolic blood pressures of the patients at a hospital are normally distributed with a mean of 138 mm Hg and a standard deviation of 12.8 mm Hg. Find the two blood pressures having these properties: the mean is midway between them and 90% of all blood pressures are between them.

Accepted Answer

The answer of The systolic blood pressures of the patients...

Question 4

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.
-Shaded area is 0.4013.

Accepted Answer

The answer of Find the indicated z score. The graph...

Question 5

The given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability.
-The probability of no more than 21 defective CD's

Accepted Answer

The continuity correction for "no more than 21" is applied by considering the area to the left of 21.5 in a normal distribution.

Question 6

Tell whether the following statistic is a biased or unbiased estimator of a population parameter: Sample proportion used to estimate a population proportion.

Accepted Answer

Sample proportion is an unbiased estimator of a population proportion because it is calculated as the number of successes divided by the total number of observations, and this ratio is an unbiased estimator of the true population proportion.

Question 7

For a standard normal distribution, find the percentage of data that are more than 2 standard deviations below the mean or more than 3 standard deviations above the mean.

Accepted Answer

According to the Empirical Rule (68-95-99.7%), almost all of the data (99.7%) falls within 3 standard deviations of the mean. Therefore, the percentage of data that are more than 2 standard deviations below the mean or more than 3 standard deviations above the mean can be calculated as the complement (100% - 99.7%) of the percentage of data that are within this range, which is approximately 0.15% + 2.15% = 2.30%. However, since we are looking for the combined percentage above and below the mean, we multiply 2.30% by 2 to get 4.60%, which is closest to option C) 2.41%. Therefore, the best choice is C).

Question 8

In a game of roulette, Jorge places 170 bets of $1 each on the number 3. A win pays off with odds 35:1 and on any one spin there is a 1/38 probability that 3 will be the winning number. Among the 170 bets, what is the minimum number of wins needed for Jorge to make a profit? Estimate the
Probability that Jorge will make a profit.

Accepted Answer

The answer of In a game of roulette, Jorge places...

Question 9

If z is a standard normal variable, find the probability.
-The probability that z lies between 0 and 3.01

Accepted Answer

The probability that a standard normal variable z lies between 0 and 3.01 is the area under the standard normal curve from 0 to 3.01. This is equal to the cumulative probability at 3.01 minus the cumulative probability at 0. The cumulative probability at 3.01 is approximately 0.9987, and at 0 it is 0.5. Therefore, the probability is 0.9987 - 0.5 = 0.4987.

Question 10

Assume that X has a normal distribution, and find the indicated probability.
-The mean is $\mu = 137.0$ and the standard deviation is $\sigma = 5.3$. Find the probability that $\mathrm { X }$ is between $134.4$ and 140.1.

Accepted Answer

The answer of Assume that X has a normal distribution,...

Question 11

For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation.
-$\mathrm { n } = 59 \text { and } \mathrm { p } = 0.7$

Accepted Answer

The normal approximation to the binomial distribution is suitable when both np and n(1-p) are greater than 5. Here, np = 59 * 0.7 = 41.3 and n(1-p) = 59 * 0.3 = 17.7, both of which are greater than 5.

Question 12

For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation.
-$\mathrm { n } = 28 \text { and } \mathrm { p } = 0.9$

Accepted Answer

The answer of For the binomial distribution with the given...

Question 13

If z is a standard normal variable, find the probability.
-The probability that z lies between $- 1.10 \text { and } - 0.36$

Accepted Answer

The probability that z lies between -1.10 and -0.36 is the area under the standard normal curve between these two values. Using a standard normal table, we find that the area to the left of -1.10 is 0.1357 and the area to the left of -0.36 is 0.3554. Therefore, the area between -1.10 and -0.36 is 0.3554 - 0.1357 = 0.2237.

Question 14

Scores on a test have a mean of $62 \text { and } Q _ { 3 } \text { is } 83 \text {. }$ . The scores have a distribution that is approximately normal. Find the standard deviation. Round your answer to the nearest tenth.

Accepted Answer

The answer of Scores on a test have a mean...

Question 15

If selecting samples of size n $\mathrm { n } \leq 30$ from a population with a known mean and standard deviation, what requirement, if any, must be satisfied in order to assume that the distribution of the sample means is a normal distribution?

Accepted Answer

For small sample sizes (n ≤ 30), the population from which samples are drawn must be normally distributed for the distribution of sample means to be approximately normal.

Question 16

Human body temperatures are normally distributed with a mean of 98.20°F and a standard deviation of 0.62°F. If 19 people are randomly selected, find the probability that their mean body temperature will be less than 98.50°F.

Accepted Answer

The standard error of the mean is 0.62/√19. Using the z-score formula, the z-score for 98.50°F is calculated and then the cumulative probability is found using the standard normal distribution table.

Question 17

The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 89 inches, and a standard deviation of 14 inches. What is the probability that the mean annual snowfall during 49 randomly picked years will exceed 91.8 inches?

Accepted Answer

The answer of The amount of snowfall falling in a...

Question 18

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
-Two percent of hair dryers produced in a certain plant are defective. Estimate the probability that of 10,000 randomly selected hair dryers, exactly 225 are defective.

Accepted Answer

The answer of Estimate the indicated probability by using the...

Question 19

For a standard normal distribution, find the percentage of data that are between 3 standard deviations below the mean and 1 standard deviation above the mean.

Accepted Answer

The answer of For a standard normal distribution, find the...

Question 20

An airline experiences a no-show rate of 6%. What is the maximum number of reservations that it could accept for a flight with a capacity of 160, if it wants the probability of accommodating all reservation holders to be at least 95%?

Accepted Answer

The answer of An airline experiences a no-show rate of...

Quiz 6: Normal Probability Distributions

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. -In one county, the conviction rate for speeding is 85%. Estimate the probability that of the next 100 speeding summonses issued, there will be at least 90 convictions.

For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. - $n = 15 \text { and } p = 0.2$

The systolic blood pressures of the patients at a hospital are normally distributed with a mean of 138 mm Hg and a standard deviation of 12.8 mm Hg. Find the two blood pressures having these properties: the mean is midway between them and 90% of all blood pressures are between them.

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. -Shaded area is 0.4013.

The given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. -The probability of no more than 21 defective CD's

Tell whether the following statistic is a biased or unbiased estimator of a population parameter: Sample proportion used to estimate a population proportion.

For a standard normal distribution, find the percentage of data that are more than 2 standard deviations below the mean or more than 3 standard deviations above the mean.

If z is a standard normal variable, find the probability. -The probability that z lies between 0 and 3.01

Assume that X has a normal distribution, and find the indicated probability. -The mean is $\mu = 137.0$ and the standard deviation is $\sigma = 5.3$ . Find the probability that $\mathrm { X }$ is between $134.4$ and 140.1.

For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. - $\mathrm { n } = 59 \text { and } \mathrm { p } = 0.7$

For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. - $\mathrm { n } = 28 \text { and } \mathrm { p } = 0.9$

If z is a standard normal variable, find the probability. -The probability that z lies between $- 1.10 \text { and } - 0.36$

Scores on a test have a mean of $62 \text { and } Q _ { 3 } \text { is } 83 \text {. }$ . The scores have a distribution that is approximately normal. Find the standard deviation. Round your answer to the nearest tenth.

If selecting samples of size n $\mathrm { n } \leq 30$ from a population with a known mean and standard deviation, what requirement, if any, must be satisfied in order to assume that the distribution of the sample means is a normal distribution?

Human body temperatures are normally distributed with a mean of 98.20°F and a standard deviation of 0.62°F. If 19 people are randomly selected, find the probability that their mean body temperature will be less than 98.50°F.

The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 89 inches, and a standard deviation of 14 inches. What is the probability that the mean annual snowfall during 49 randomly picked years will exceed 91.8 inches?

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. -Two percent of hair dryers produced in a certain plant are defective. Estimate the probability that of 10,000 randomly selected hair dryers, exactly 225 are defective.

For a standard normal distribution, find the percentage of data that are between 3 standard deviations below the mean and 1 standard deviation above the mean.

An airline experiences a no-show rate of 6%. What is the maximum number of reservations that it could accept for a flight with a capacity of 160, if it wants the probability of accommodating all reservation holders to be at least 95%?

Quiz 6: Normal Probability Distributions

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. -In one county, the conviction rate for speeding is 85%. Estimate the probability that of the next 100 speeding summonses issued, there will be at least 90 convictions.

For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. - n=15 and p=0.2n = 15 \text { and } p = 0.2n=15 and p=0.2

The systolic blood pressures of the patients at a hospital are normally distributed with a mean of 138 mm Hg and a standard deviation of 12.8 mm Hg. Find the two blood pressures having these properties: the mean is midway between them and 90% of all blood pressures are between them.

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. -Shaded area is 0.4013.

The given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. -The probability of no more than 21 defective CD's

Tell whether the following statistic is a biased or unbiased estimator of a population parameter: Sample proportion used to estimate a population proportion.

For a standard normal distribution, find the percentage of data that are more than 2 standard deviations below the mean or more than 3 standard deviations above the mean.

If z is a standard normal variable, find the probability. -The probability that z lies between 0 and 3.01

Assume that X has a normal distribution, and find the indicated probability. -The mean is μ=137.0\mu = 137.0μ=137.0 and the standard deviation is σ=5.3\sigma = 5.3σ=5.3 . Find the probability that X\mathrm { X }X is between 134.4134.4134.4 and 140.1.

For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. - n=59 and p=0.7\mathrm { n } = 59 \text { and } \mathrm { p } = 0.7n=59 and p=0.7

For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. - n=28 and p=0.9\mathrm { n } = 28 \text { and } \mathrm { p } = 0.9n=28 and p=0.9

If z is a standard normal variable, find the probability. -The probability that z lies between −1.10 and −0.36- 1.10 \text { and } - 0.36−1.10 and −0.36

Scores on a test have a mean of 62 and Q3 is 83. 62 \text { and } Q _ { 3 } \text { is } 83 \text {. }62 and Q3​ is 83. . The scores have a distribution that is approximately normal. Find the standard deviation. Round your answer to the nearest tenth.

If selecting samples of size n n≤30\mathrm { n } \leq 30n≤30 from a population with a known mean and standard deviation, what requirement, if any, must be satisfied in order to assume that the distribution of the sample means is a normal distribution?

Human body temperatures are normally distributed with a mean of 98.20°F and a standard deviation of 0.62°F. If 19 people are randomly selected, find the probability that their mean body temperature will be less than 98.50°F.

The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 89 inches, and a standard deviation of 14 inches. What is the probability that the mean annual snowfall during 49 randomly picked years will exceed 91.8 inches?

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. -Two percent of hair dryers produced in a certain plant are defective. Estimate the probability that of 10,000 randomly selected hair dryers, exactly 225 are defective.

For a standard normal distribution, find the percentage of data that are between 3 standard deviations below the mean and 1 standard deviation above the mean.

An airline experiences a no-show rate of 6%. What is the maximum number of reservations that it could accept for a flight with a capacity of 160, if it wants the probability of accommodating all reservation holders to be at least 95%?

For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. - $n = 15 \text { and } p = 0.2$

Assume that X has a normal distribution, and find the indicated probability. -The mean is $\mu = 137.0$ and the standard deviation is $\sigma = 5.3$ . Find the probability that $\mathrm { X }$ is between $134.4$ and 140.1.

For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. - $\mathrm { n } = 59 \text { and } \mathrm { p } = 0.7$

For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. - $\mathrm { n } = 28 \text { and } \mathrm { p } = 0.9$

If z is a standard normal variable, find the probability. -The probability that z lies between $- 1.10 \text { and } - 0.36$

Scores on a test have a mean of $62 \text { and } Q _ { 3 } \text { is } 83 \text {. }$ . The scores have a distribution that is approximately normal. Find the standard deviation. Round your answer to the nearest tenth.

If selecting samples of size n $\mathrm { n } \leq 30$ from a population with a known mean and standard deviation, what requirement, if any, must be satisfied in order to assume that the distribution of the sample means is a normal distribution?