Exam 4: The Normal Distributions

Using the standard Normal distribution tables, what is the area under the standard Normal curve corresponding to Z < 0.75?

Running times for 400 meters are Normally distributed for young men between 18 and 30 years of age, with a mean of 93 seconds and a standard deviation of 16 seconds. What would a man's running time have to be to put him in the top 1% of runners?

Your friend took an introductory statistics class last year and learned all about density curves. He draws a smooth curve with a long left tail. For such a curve, which of the following is true for the mean and median?

The typical college freshman spends an average of  = 150 minutes per day, with a standard deviation of  = 50 minutes, on social media. The distribution of time on social media is known to be Normal. The median of the distribution is:

A company produces packets of soap powder labeled "Giant Size 32 Ounces." The actual weight of soap powder in such a box has a Normal distribution, with a mean of 33 oz and a standard deviation of 0.7 oz. To avoid having dissatisfied customers, the company says a box of soap is considered underweight if it weighs less than 32 oz. To avoid losing money, it labels the top 5% (the heaviest 5%) overweight. What proportion of boxes is underweight (weighs less than 32 oz)?

You recently took a statistics exam in a large class. The instructor tells the class that the scores were Normally distributed, with a mean of 72 (out of 100) and a standard deviation of 12. Your score was 96. You would like to know what proportion of students did better than you did. Unfortunately, your calculator batteries are dead and you must now rely on Normal tables. You need to find which of the following?

The average time taken for your Internet service provider to remotely resolve a trouble ticket has a Normal distribution, with a mean of 4.3 hours and a standard deviation of 3.1 hours. What percent of the time can you expect to wait longer than a full (8-hour) business day for a resolution?

A company produces packets of soap powder labeled "Giant Size 32 Ounces." The actual weight of soap powder in such a box has a Normal distribution, with a mean of 33 oz and a standard deviation of 0.7 oz. To avoid having dissatisfied customers, the company says a box of soap is considered underweight if it weighs less than 32 oz. To avoid losing money, it labels the top 5% (the heaviest 5%) overweight. How heavy does a box have to be for it to be labeled overweight?

The typical college freshman spends an average of  = 150 minutes per day, with a standard deviation of  = 50 minutes, on social media. The distribution of time on social media is known to be Normal. The third quartile is:

The graph below shows a distribution that is called a chi-squared distribution. For this distribution, the median:

A high-profile consulting company chooses its new entry-level employees from a pool of recent college graduates using a five-step interview process. Unfortunately, there are usually more candidates who complete the interview process than the number of new positions that are available. As a result, cumulative GPA is used as a tie-breaker. GPAs for the successful interviewees are Normally distributed, with a mean of 3.3 and a standard deviation of 0.4. Out of the163 people who made it through the interview process, only 121 can be hired. What cut-off GPA should the company use?

Suppose you received a score of 91 out of 100 on exam 1. The mean was 79 and the standard deviation was 8. What score do you need on exam 2 to do equally well, if the mean is 60 and the standard deviation is 12?

Scores on the SAT verbal test in recent years follow approximately the N(515, 109) distribution. The proportion of students scoring at least 600 is closest to:

The typical college freshman spends an average of  = 150 minutes per day, with a standard deviation of  = 50 minutes, on social media. The distribution of time on social media is known to be Normal. The proportion of students spending at least 2 hours on social media equals:

Suppose you received a score of 95 out of 100 on exam 1. The mean was 79 and the standard deviation was 8. If your score on exam 2 is 90 out of 100, and the mean was 60 with a standard deviation of 15, then you did:

Your friend took an introductory statistics class last year and learned all about density curves. She tells you that two requirements of a density curve are:

Scores on the SAT verbal test in recent years follow approximately the N(515, 109) distribution. The proportion of students scoring between 460 and 550 is closest to:

Running times for 400 meters are Normally distributed for young men between 18 and 30 years of age, with a mean of 93 seconds and a standard deviation of 16 seconds. Thus, 99.7% of running times are approximately between:

The average time taken for your Internet service provider to remotely resolve a trouble ticket has a Normal distribution, with a mean of 4.3 hours and a standard deviation of 3.1 hours. What percentage of the tickets are resolved in less than half an hour?

A cappuccino vending machine is designed to dispense an average of  oz per cup. If the ounces per fill are Normally distributed, with a standard deviation of 0.4 oz, at what value should  be set so that 6 oz cups will overflow only 2% of the time?