Question 1

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Shaded area is 0.4483.

Accepted Answer

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

Question 2

The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0°C at the freezing point of water. Tests on a large sample of these
Thermometers reveal that at the freezing point of water, some give readings below 0°C
(denoted by negative numbers)and some give readings above 0°C (denoted by positive
Numbers). Assume that the mean reading is 0°C and the standard deviation of the readings is
1.00°C. Also assume that the frequency distribution of errors closely resembles the normal
Distribution. A thermometer is randomly selected and tested. A quality control analyst wants
To examine thermometers that give readings in the bottom 4%. Find the temperature reading
That separates the bottom 4% from the others.

Accepted Answer

The answer of The Precision Scientific Instrument Company manufactures thermometers...

Question 3

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 35 defective CDs

Accepted Answer

Since the given values are discrete, we use continuity correction to adjust for the fact that the normal distribution is continuous. In this case, we are looking for the probability of no more than 35 defective CDs, so we need to shade the area to the left of 35.5 on the normal distribution curve. This is because if we consider the discrete value of 35, the area to the left of 35 includes all values up to and including 35. However, in the continuous normal distribution, the probability of getting exactly 35 is infinitesimally small, and we need to consider the area up to 35.5 to include the probability of getting 35 or less. Therefore, the best choice is B.

Question 4

Assume that the red blood cell counts of women are normally distributed with a mean of 4.577 million cells per microliter and a standard deviation of 0.382 million cells per
Microliter. Find the value closest to the probability that a randomly selected woman has a red
Blood cell count above the normal range of 4.2 to 5.4 million cells per microliter.

Accepted Answer

The answer of Assume that the red blood cell counts...

Question 5

The probability that a radish seed will germinate is 0.7. Estimate the probability that of 140 randomly selected seeds, exactly 100 will germinate.

Accepted Answer

The probability of getting exactly 100 germinating seeds out of 140 can be calculated using the binomial distribution formula:

P(X = 100) = (140 choose 100) * (0.7)^100 * (0.3)^40

Using a calculator, we get P(X = 100) ≈ 0.0669. Therefore, the best choice is C.

Question 6

A baseball player has a batting average of 0.346, so the probability of a hit is 0.346. Assume that his hitting attempts are independent of each other. Assume that the batter gets up to bat 4
Times in each game. Estimate the probability that in 50 consecutive games, there are at least
45 games in which the batter gets at least one hit. (Hint: first find the probability that in one
Game the batter gets at least one hit)

Accepted Answer

The probability of getting at least one hit in one game is 1 - (1 - 0.346)^4 = 0.918. The probability of getting at least one hit in 50 consecutive games is (0.918)^50 = 0.0918.

Question 7

In a population of 210 women, the heights of the women are normally distributed with a mean of  64.4  inches and a standard deviation of  2.9  inches. If 36 women are selected at random, find the mean $\mu _ { \bar { x } }$ and standard deviation $\sigma _ { \bar { x } }$ of the population of sample means. Assume that the sampling is done without replacement and use a finite population correction factor.

Accepted Answer

The answer of In a population of 210 women, the...

Question 8

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the
Probability of a rating that is between 200 and 275.

Accepted Answer

To find the probability of a rating between 200 and 275, we use the Z-score formula: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation. For X = 275, Z = (275 - 200) / 50 = 1.5. Using the Z-table, the probability of Z being less than 1.5 is approximately 0.9332. Since the probability of a score being less than the mean (200) is 0.5 (due to the symmetry of the normal distribution), the probability of a score between 200 and 275 is 0.9332 - 0.5 = 0.4332.

Question 9

Which of the following is a biased estimator?

Accepted Answer

The answer of Which of the following is a biased...

Question 10

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

Accepted Answer

The answer of Find the area of the shaded region....

Question 11

A coin is tossed 20 times. A person who claims to have extrasensory perception is asked to predict the outcome of each flip in advance. She predicts correctly on 14 tosses. What is the
Probability of being correct 14 or more times by guessing? Does this probability seem to
Verify her claim? Use the normal distribution to approximate the desired probability.

Accepted Answer

The probability of guessing correctly 14 or more times out of 20 by chance is approximately 0.0582, which is relatively low, suggesting that the result could be due to something other than random guessing, but it does not strongly verify her claim of extrasensory perception.

Question 12

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, at least 219
Are defective.

Accepted Answer

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

Question 13

If  z  is a standard normal variable, find the probability:  P(-0.73<z<2.27)

Accepted Answer

To find the probability that $z$ is between -0.73 and 2.27, we look up the corresponding values in the standard normal distribution table or use a calculator. The value for $z = 2.27$ is approximately 0.9883 and for $z = -0.73$ is approximately 0.2327. Subtracting these gives $0.9883 - 0.2327 = 0.7556$, which rounds to 0.7557, indicating the probability of $z$ being between -0.73 and 2.27.

Question 14

Scores on a test are normally distributed with a mean of  63.2  and a standard deviation of  11.7 . Find $P _ { 81 } ,$ which separates the bottom  81%  from the top  19% .

Accepted Answer

To find $P_{81}$, which separates the bottom 81% from the top 19%, we use the Z-score formula and the normal distribution properties. Given the mean ($\mu$) is 63.2 and the standard deviation ($\sigma$) is 11.7, we look for the Z-score corresponding to the 81st percentile in the standard normal distribution table. The Z-score for 81% (or 0.81 probability) is approximately 0.88. We then apply the formula: $X = \mu + Z\sigma$, where $X$ is the score we're looking for. Substituting the values, $X = 63.2 + 0.88 \times 11.7$, we get approximately 73.5.

Question 15

In one region, the September energy consumption levels for single -family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. For a
Randomly selected home, find the probability that the September energy consumption level is
Between 1100 kWh and 1225 kWh.

Accepted Answer

The answer of In one region, the September energy consumption...

Question 16

Assume that the red blood cell counts of women are normally distributed with a mean of 4.577 million cells per microliter and a standard deviation of 0.382 million cells per
Microliter. Approximately what percentage of women have red blood cell counts in the
Normal range from 4.2 to 5.4 million cells per microliter?

Accepted Answer

To find the percentage of women with red blood cell counts in the normal range from 4.2 to 5.4 million cells per microliter, we use the properties of the normal distribution. First, we calculate the z-scores for the lower and upper limits of the range:- For 4.2 million cells/μL: $Z = \frac{4.2 - 4.577}{0.382} \approx -0.987$- For 5.4 million cells/μL: $Z = \frac{5.4 - 4.577}{0.382} \approx 2.151$Using standard normal distribution tables or a calculator, we find the probabilities corresponding to these z-scores:- The area to the left of $Z = -0.987$ is approximately 0.1619 (16.19%).- The area to the left of $Z = 2.151$ is approximately 0.9842 (98.42%).To find the percentage of women within this range, we subtract the lower percentage from the higher percentage: $98.42\% - 16.19\% = 82.23\%$.This calculation shows that approximately 82.31% of women have red blood cell counts within the normal range of 4.2 to 5.4 million cells per microliter, which corresponds to choice A.

Question 17

Assume that the red blood cell counts of women are normally distributed with a mean of 4.577 million cells per microliter and a standard deviation of 0.382 million cells per
Microliter. Find the 80th percentile for the red blood cell counts of women.

Accepted Answer

The 80th percentile corresponds to a z-score of approximately 0.84. Using the formula X = μ + zσ, where μ is the mean and σ is the standard deviation, we calculate X = 4.577 + 0.84(0.382) = 4.898 million cells per microliter.

Question 18

The weights of college football players are normally distributed with a mean of 200 pounds and a standard deviation of 50 pounds. If a college football player is randomly selected, find
The probability that he weighs between 170 and 220 pounds.

Accepted Answer

To find the probability that a player weighs between 170 and 220 pounds, we use the Z-score formula: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation. For X = 170, Z = (170 - 200) / 50 = -0.6. For X = 220, Z = (220 - 200) / 50 = 0.4. Looking these Z-scores up in a standard normal distribution table or using a calculator, we find the probabilities for Z = -0.6 and Z = 0.4, then subtract the smaller from the larger to find the probability of being between these two Z-scores. This calculation gives us approximately 0.3811, indicating the probability a randomly selected player weighs between 170 and 220 pounds.

Question 19

An unbiased estimator is a statistic that targets the value of the of the population parameter such that the sampling distribution of the statistic has a __________equal to the _________ of
The corresponding parameter.

Accepted Answer

An unbiased estimator is defined as a statistic where the mean of its sampling distribution is equal to the true mean of the population parameter it estimates. This means that, on average, the estimator hits the target parameter.

Question 20

If  z  is a standard normal variable, find  P(z>0.97) .

Accepted Answer

The answer of If  z  is a standard...

Quiz 6: Normal Probability Distributions

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Shaded area is 0.4483.

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 35 defective CDs

The probability that a radish seed will germinate is 0.7. Estimate the probability that of 140 randomly selected seeds, exactly 100 will germinate.

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the Probability of a rating that is between 200 and 275.

Which of the following is a biased estimator?

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

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, at least 219 Are defective.

If z is a standard normal variable, find the probability: P(-0.73<z<2.27)

Scores on a test are normally distributed with a mean of 63.2 and a standard deviation of 11.7 . Find $P _ { 81 } ,$ which separates the bottom 81% from the top 19% .

Assume that the red blood cell counts of women are normally distributed with a mean of 4.577 million cells per microliter and a standard deviation of 0.382 million cells per Microliter. Find the 80th percentile for the red blood cell counts of women.

The weights of college football players are normally distributed with a mean of 200 pounds and a standard deviation of 50 pounds. If a college football player is randomly selected, find The probability that he weighs between 170 and 220 pounds.

An unbiased estimator is a statistic that targets the value of the of the population parameter such that the sampling distribution of the statistic has a __equal to the _ of The corresponding parameter.

If z is a standard normal variable, find P(z>0.97) .

Quiz 6: Normal Probability Distributions

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Shaded area is 0.4483.

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 35 defective CDs

The probability that a radish seed will germinate is 0.7. Estimate the probability that of 140 randomly selected seeds, exactly 100 will germinate.

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the Probability of a rating that is between 200 and 275.

Which of the following is a biased estimator?

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

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, at least 219 Are defective.

If z is a standard normal variable, find the probability: P(-0.73<z<2.27)

Scores on a test are normally distributed with a mean of 63.2 and a standard deviation of 11.7 . Find P81,P _ { 81 } ,P81​, which separates the bottom 81% from the top 19% .

Assume that the red blood cell counts of women are normally distributed with a mean of 4.577 million cells per microliter and a standard deviation of 0.382 million cells per Microliter. Find the 80th percentile for the red blood cell counts of women.

The weights of college football players are normally distributed with a mean of 200 pounds and a standard deviation of 50 pounds. If a college football player is randomly selected, find The probability that he weighs between 170 and 220 pounds.

An unbiased estimator is a statistic that targets the value of the of the population parameter such that the sampling distribution of the statistic has a __________equal to the _________ of The corresponding parameter.

If z is a standard normal variable, find P(z>0.97) .

Scores on a test are normally distributed with a mean of 63.2 and a standard deviation of 11.7 . Find $P _ { 81 } ,$ which separates the bottom 81% from the top 19% .

An unbiased estimator is a statistic that targets the value of the of the population parameter such that the sampling distribution of the statistic has a __equal to the _ of The corresponding parameter.