Unit Test — Unit test Answers

Records show that Oliver is typically 10–30 minutes late for his shift at work. The distribution for the minutes he is late forms a consistent pattern, which can be graphed as the given uniform density curve.

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 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.

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.

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

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?

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.

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

Consider the given density curve.

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.

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.

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.

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?

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

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?

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.

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.

A curve goes from 8 to 20 on the x-axis.

2 graphs. Graph A: a dotted line goes from (1, 0) to (1, 0.25), is solid and horizontal to (2, 0.25), is dotted to (2, negative 0.1875), is solid and horizontal to (6, negative 0.1875), and then is dotted to (6, 0). Graph B. A line goes from (negative 5, 0) to (negative 3, 0.25), and then decreases to (3, 0).