Finding Areas within a Normal Distribution — Unit test Answers

A machine at a food-distribution factory fills boxes of rice. The distribution of the weights of filled boxes of rice has an approximately Normal distribution, with a mean of 28.2 ounces and a standard deviation of 0.4 ounces. Boxes are often weighed before shipping, and any box with a weight of at most 27.5 ounces is considered underweight and is rejected for distribution. What percentage of filled boxes of rice are rejected for distribution?Find the z-table here.

The graph shows the distribution of the number of text messages young adults send per day.

The weights of a pack of chewing gum for a certain brand have a mean of 47.1 grams and a standard deviation of 2.4 grams. What is the weight of a randomly selected pack of gum that has a z-score of 3.11?

The daily high temperatures in a vacation resort city are approximately Normal, with a mean temperature of 75 degrees Fahrenheit and a standard deviation of 6 degrees. What percentage of days have a high temperature between 66 and 80 degrees?Find the z-table here.

Scores on a national math test are Normally distributed, with a mean score of 490 and a standard deviation of 50. Katlyn’s math score is in the 92nd percentile. What is her math score, rounded to the nearest whole number?Find the z-table here.

In a standard Normal distribution, which z-score represents the 20th percentile?Find the z-table here.

A runner’s distribution of times for running 1,000 meters has a mean of 4.5 minutes with a standard deviation of 0.75 minutes. One of the runner’s times has a z-score of –1.08. Which of the following statements is the best interpretation of this z-score?

The graph shows the distribution of the amount of time (in minutes) people spend watching TV shows on a popular streaming service. The distribution is approximately Normal, with a mean of 71 minutes and a standard deviation of 15 minutes.

At the Fisher farm, the weights of zucchini squash are Normally distributed. Which standardized weight represents the top 10% of the zucchinis?Find the z-table here.

Bags of flour at a local grocery store have a mean weight of 83 ounces with a standard deviation of 2 ounces. Which weight represents the 65th percentile?Find the z-table here.

In a standard Normal distribution, what proportion of observations lie below z = 0.18?Find the z-table here.

The graph shows the distribution of the cost of drinks at a popular coffee shop. The distribution is approximately Normal, with a mean of $3.34 and a standard deviation of $0.75.

For the 1,000-meter running event, Abby’s mean time is 4.5 minutes with a standard deviation of 0.75 minutes. For the 800-meter event, Abby’s mean time is 3.2 minutes with a standard deviation of 0.4 minutes. In the last track meet, Abby ran the 1,000-meter race in 4.1 minutes and the 800-meter race in 3 minutes. In which event did Abby have a better performance?

The graph shows the distribution of the lengths (in seconds) of videos on a popular video-streaming site. The distribution is approximately Normal, with a mean of 264 seconds and a standard deviation of 75 seconds.

On a unit test in a statistics class, the teacher determines that the mean test grade was 77.5 with a standard deviation of 5.2. One student’s test grade was 91. What is the z-score for the student’s test?

In a standard Normal distribution, what percentage of observations lie above z = 0.16?Find the z-table here.

In a standard Normal distribution, what percentage of observations lie between z = 0.37 and z = 1.65?Find the z-table here.

The graph shows the distribution of the amount of time (in minutes) people spend watching TV shows on a popular streaming service. The distribution is approximately Normal, with a mean of 71 minutes and a standard deviation of 15 minutes.

At the Fisher farm, the weights of zucchini squash are Normally distributed, with a mean of 5 ounces and a standard deviation of 0.7 ounces. Which weight represents the top 10% of the zucchinis?Find the z-table here.

A teacher gave a unit test to both of her statistics classes. The mean test grade for Class A was 77 points, with a standard deviation of 5 points, whereas the mean test grade for Class B was 80, with a standard deviation of 7 points. Kyle, in Class A, received an 82 on the test, and Caleb, in Class B, received an 87. Whose performance on the unit test was better relative to their class?