Finding Areas within a Normal Distribution — Unit test Answers

The diameters of cherry tomatoes produced by a large farm have an approximately Normal distribution, with a mean diameter of 22 mm and a standard deviation of 2.5 mm. After they are picked and washed, tomatoes with a diameter of at most 15 mm or at least 30 mm are rejected and not sold. What proportion of such tomatoes are rejected?Find the z-table here.

In a statistics class, students were asked how many siblings they have. Their responses are shown.2, 3, 1, 3, 5, 3, 3, 3, 6, 3, 5, 0, 3

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.

Keeping car tires inflated is essential to safe driving. For one type of car tire, the tire pressure in pounds per square inch (psi) is assumed to be approximately Normal, with a mean of 35 psi and a standard deviation of 2 psi. What percentage of tires are inflated to a pressure between 33.5 and 36 psi?Find the z-table here.

In a statistics class, students were asked how many siblings they have. The mean number of siblings for the class is 3.08 with a standard deviation of 1.61 siblings. The z-score for a student with four siblings is 0.57. Which of the following statements is the best interpretation of the z-score?

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. If a weather forecast predicts the high temperature will be at most 68 degrees, the city provides fewer lifeguards for the city beaches. On what percentage of days will fewer lifeguards be provided?Find the z-table here.

Kaitlyn and Allison took a standardized algebra test in different states. Kaitlyn takes the test for Virginia and scores a 458. Allison takes the test for North Carolina and scores a 185. Suppose the mean and standard deviation for the algebra scores for Virginia are 405 and 30, respectively, and the mean and standard deviation for the algebra scores for North Carolina are 152 and 20, respectively. Which student did better on her algebra test?

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

In a certain breed of cattle, the length of gestation has a mean of 284 days and a standard deviation of 5.5 days. What is the length of the gestation period, to the nearest whole number, that is 0.7 standard deviations below the mean?

In a standard Normal distribution, what proportion of observations lie between z = 0.15 and z = 1.20?Find the z-table here.

The graph shows the distribution of weights (in pounds) for male duck-billed platypuses.

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.

The salt content in snack bags of pretzels is Normally distributed, with a mean of 180 mg and a standard deviation of 15 mg. Eighty four percent of bags have a salt content lower than which value?Find the z-table here.

The times for running a 5K for a local charity event are Normally distributed. Which standardized time represents the fastest 3%?Find the z-table here.

In a standard Normal distribution, 1.5% of observations lie above which z-score?Find the z-table here.