Question 1

Which set of data represented by the three histograms below most likely came from a normal distribution?

Accepted Answer

The answer of Which set of data represented by the...

Question 2

The scores on a certain test are normally distributed with a mean score of 58 and a standard deviation of 4. What is the likelihood that a sample of 90 students will have a mean score of at least 58.4216?

Accepted Answer

The answer of The scores on a certain test are...

Question 3

Decide which of the described variables is/are likely have a normal or near-normal distribution.
a. The heights of corn stalks in one row of corn that is half a mile long
b.The numbers of viewers of each of the channels from 202 to 550 on Direct TV at 7:00
PM CDT on the third Thursday of November 2012 (349 data values)

Accepted Answer

The heights of corn stalks in a row are likely to be normally distributed due to natural biological variation, while TV viewership numbers are often skewed or follow other distributions.

Question 4

Standard used car prices are based on the assumption that a car will be driven an average of 12,000 miles per year. If the standard deviation is 2000 miles, approximately what percent of cars will be driven between 8000 and 16,000 miles per year?

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The answer of Standard used car prices are based on...

Question 5

Assume that women have heights that are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. Find the 60th percentile.

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The answer of Assume that women have heights that are...

Question 6

Which one of the three variables below is most likely to be normally or nearly normally distributed?

Accepted Answer

The lengths of randomly selected white pine needles are likely to be normally distributed due to natural biological variation, whereas dice throws and people in line are discrete and not typically normally distributed.

Question 7

A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.77 hours.
Assume that a random sample of 40 mechanics is selected and the mean rebuild time of the sample is computed. Assuming the mean times are normally distributed, what percentage of sample means are greater than 9.1 hours?

Accepted Answer

The standard error of the mean is calculated as the standard deviation divided by the square root of the sample size. Using this, we find the z-score for 9.1 hours and then use the standard normal distribution to find the percentage of sample means greater than 9.1 hours.

Question 8

If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard
deviation of 500 hours, what percent of the bulbs will not last as long as 2000 hours?
Apply the 68-95-99.7 rule to answer #4 and #5.

Accepted Answer

The answer of If light bulbs have lives that are...

Question 9

If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, approximately what percentage of light bulbs has a life of more than 3000 hours?

Accepted Answer

A life of 3000 hours is 1 standard deviation above the mean (2500 + 500). In a normal distribution, approximately 68% of the data falls within 1 standard deviation of the mean, leaving 32% outside this range. Since the distribution is symmetric, about 16% of the data is more than 1 standard deviation above the mean.

Question 10

The mean score on the exit examination for an urban high school is 63 with a standard deviation of 8. What is the mean of the distribution of sample means with a sample size of 9?

Accepted Answer

The answer of The mean score on the exit examination...

Question 11

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 225 and 275.

Accepted Answer

The answer of A bank's loan officer rates applicants for...

Question 12

Apply the 68-95-99.7 rule to answer 
-The annual precipitation for one city is normally distributed with a mean of 28 inches and a standard deviation of 3.4 inches. Fill in the blanks. in 95% of the years, the precipitation in this city is between _____ and _____ inches.

Accepted Answer

The answer of Apply the 68-95-99.7 rule to answer 
-The...

Question 13

The mean score on the exit examination for an urban high school is 63 with a standard deviation of 9. What is the standard deviation of the distribution of sample means with a sample size of 9?

Accepted Answer

The answer of The mean score on the exit examination...

Question 14

There are over 1200 species of inchworms indigenous to North America. Some have been taken to the space station while others provided the idea for neon inchworms from the Jelly Belly Candy Company. One species has a mean length of 0.98 inches and a standard deviation of 0.05 inches. The lengths of 99.7% of these worms will be between ________ and _________ inches.

Accepted Answer

The answer of There are over 1200 species of inchworms...

Question 15

A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.77 hours.
Assume that a random sample of 40 mechanics is selected and the mean rebuild time of the sample is computed. Assuming the mean times are normally distributed, what percentage of sample means are greater than 7.7 hours?

Accepted Answer

The standard error of the mean is 1.77/sqrt(40). The z-score for 7.7 hours is calculated using the formula (7.7 - 8.4) / (1.77/sqrt(40)). The z-score is approximately -2.67. Using the standard normal distribution table, the percentage of sample means greater than 7.7 hours is about 99.38%.

Question 16

The area under the standard normal curve between 1 and 2 is equal to 0.1359. Scores on a particular aptitude test are normally distributed with a mean of 100 and a standard deviation of 10. Which of the following are equal to 13.59%?
a. The percentage of scores between 120 and 130
b. The percentage of scores between 110 and 120
c. The percentage of scores between 80 and 90
d. The percentage of scores between 90 and 120
e. The percentage of scores between 90 and 110

Accepted Answer

The answer of The area under the standard normal curve...

Question 17

Apply the 68-95-99.7 rule to answer 
-The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mm Hg and a standard deviation of 12 mm Hg. What percentage of 18-year-old women have a systolic blood pressure that is within 3 standard deviations of the mean on either side?

Accepted Answer

The answer of Apply the 68-95-99.7 rule to answer 
-The...

Question 18

A math teacher gives two different tests to measure students' aptitude for math. Scores on the first test are normally distributed with a mean of 24 and a standard deviation of 4.5. Scores on the second test are normally distributed with a mean of 70 and a standard deviation of 11.3.
Assume that the two tests use different scales to measure the same aptitude. If a student scores 29 on the first test, what would be his equivalent score on the second test? (That is, find the score that would put him in the same percentile.)

Accepted Answer

The answer of A math teacher gives two different tests...

Question 19

The weights of the fish in a certain lake are normally distributed with a mean of 20 lb and a standard deviation of 6. If 9 fish are randomly selected, what is the likelihood that the mean weight will be between 17.6 and 21.6 lb?

Accepted Answer

The answer of The weights of the fish in a...

Question 20

Select the distribution that appears to be the most normal.

Accepted Answer

The answer of Select the distribution that appears to be...

Quiz 5: A Normal World

Which set of data represented by the three histograms below most likely came from a normal distribution?

The scores on a certain test are normally distributed with a mean score of 58 and a standard deviation of 4. What is the likelihood that a sample of 90 students will have a mean score of at least 58.4216?

Standard used car prices are based on the assumption that a car will be driven an average of 12,000 miles per year. If the standard deviation is 2000 miles, approximately what percent of cars will be driven between 8000 and 16,000 miles per year?

Assume that women have heights that are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. Find the 60th percentile.

Which one of the three variables below is most likely to be normally or nearly normally distributed?

If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, what percent of the bulbs will not last as long as 2000 hours? Apply the 68-95-99.7 rule to answer #4 and #5.

If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, approximately what percentage of light bulbs has a life of more than 3000 hours?

The mean score on the exit examination for an urban high school is 63 with a standard deviation of 8. What is the mean of the distribution of sample means with a sample size of 9?

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 225 and 275.

Apply the 68-95-99.7 rule to answer -The annual precipitation for one city is normally distributed with a mean of 28 inches and a standard deviation of 3.4 inches. Fill in the blanks. in 95% of the years, the precipitation in this city is between _ and _ inches.

The mean score on the exit examination for an urban high school is 63 with a standard deviation of 9. What is the standard deviation of the distribution of sample means with a sample size of 9?

The weights of the fish in a certain lake are normally distributed with a mean of 20 lb and a standard deviation of 6. If 9 fish are randomly selected, what is the likelihood that the mean weight will be between 17.6 and 21.6 lb?

Select the distribution that appears to be the most normal.

Quiz 5: A Normal World

Which set of data represented by the three histograms below most likely came from a normal distribution?

The scores on a certain test are normally distributed with a mean score of 58 and a standard deviation of 4. What is the likelihood that a sample of 90 students will have a mean score of at least 58.4216?

Standard used car prices are based on the assumption that a car will be driven an average of 12,000 miles per year. If the standard deviation is 2000 miles, approximately what percent of cars will be driven between 8000 and 16,000 miles per year?

Assume that women have heights that are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. Find the 60th percentile.

Which one of the three variables below is most likely to be normally or nearly normally distributed?

If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, what percent of the bulbs will not last as long as 2000 hours? Apply the 68-95-99.7 rule to answer #4 and #5.

If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, approximately what percentage of light bulbs has a life of more than 3000 hours?

The mean score on the exit examination for an urban high school is 63 with a standard deviation of 8. What is the mean of the distribution of sample means with a sample size of 9?

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 225 and 275.

Apply the 68-95-99.7 rule to answer -The annual precipitation for one city is normally distributed with a mean of 28 inches and a standard deviation of 3.4 inches. Fill in the blanks. in 95% of the years, the precipitation in this city is between _____ and _____ inches.

The mean score on the exit examination for an urban high school is 63 with a standard deviation of 9. What is the standard deviation of the distribution of sample means with a sample size of 9?

The weights of the fish in a certain lake are normally distributed with a mean of 20 lb and a standard deviation of 6. If 9 fish are randomly selected, what is the likelihood that the mean weight will be between 17.6 and 21.6 lb?

Select the distribution that appears to be the most normal.

Apply the 68-95-99.7 rule to answer -The annual precipitation for one city is normally distributed with a mean of 28 inches and a standard deviation of 3.4 inches. Fill in the blanks. in 95% of the years, the precipitation in this city is between _ and _ inches.