Exam 6: The Normal Probability Distribution

Tabulation of a strike vote showed that 90% of those voting cast their ballot in favour of strike action. You take a sample of 50 voters. Assume this to be a binomial distribution. What is the probability that more than 45 of the voters from your sample voted in favour of strike action?

A statistics student receives a grade of 85 on a statistics midterm. If the corresponding z-score equals +1.5 and the standard deviation equals 7, the average grade on this exam is .

i. For a normal probability distribution, about 95 percent of the area under normal curve is within plus and minus two standard deviations of the mean and practically all (99.73 percent) of the area under the normal curve is within three standard deviations of the mean. Ii) The total area under the normal curve is 100%. Iii) The mean of a normal probability distribution is 500 and the standard deviation is 10. About 95 percent of the observations lie between 480 and 520.

A sample of 500 evening students revealed that their annual incomes were normally distributed with a mean income of $50,000 and a standard deviation of $4,000. How many students earned less than $45,000?

Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years, (based on data from "Getting Things Fixed," Consumer Reports). -One classic use of the normal distribution is inspired by a letter to Dear Abbey in which a wife claimed to have given birth 308 days after a brief visit from her husband, who was serving in the Navy. The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. Given this information, the probability of a pregnancy lasting 308 days or longer is _____. The result suggests that the husband ( (is/is not) ) the father of the child.

A random variable from an experiment where outcomes are normally distributed

The area under a normal curve to the right of a z-score of zero is a proportion of________ .

Management is considering adopting a bonus system to increase production. One suggestion is to pay a bonus on the highest 5 percent of production based on past experience. Past records indicate that, on the average, 4,000 units of a small assembly are produced during a week. The distribution of the weekly production is approximately normally distributed with a standard deviation of 60 units. If the bonus is paid on the upper 5 percent of production, the bonus will be paid on how many units or more?

The average score of 100 students taking a statistics final was 70 with a standard deviation of 7. Assuming a normal distribution, approximately how many scored greater than 65?

Past experience of a large manufacturing firm with administering a test to recent college graduates who had applied for a job revealed that the mean test score was 500, and the standard deviation was 50. The distribution of the test scores was normal. Based on this experience, management is considering placing a person whose score is in the upper 6 percent of the distribution directly into a responsible position. What is the lowest score a college graduate must earn to qualify for a responsible position?

From past history, the scores on a statistics test are normally distributed with a mean of 70% and a standard deviation of 5%. To earn a "B" on the test, a student must be in the top 15% of the class. What should a student score to receive a "B"?

The standard normal probability distribution is one which has:

Bottomline Ink, a forms management company, fills 100 orders a day with a 2% error rate in the completed orders. Assume this to be a binomial distribution. What is the probability that there will be more than 5 order errors in a given day?

A sample of 500 evening students revealed that their annual incomes from employment in industry during the day were normally distributed with a mean income of $30,000 and a standard deviation of $3,000. -_______students earned more than $30,000?

Tabulation of a strike vote showed that 90% of those voting cast their ballot in favour of strike action. You take a sample of 50 voters. Assume this to be a binomial distribution. What is the standard deviation for this distribution?

i. For a normal probability distribution, about 95 percent of the area under normal curve is within plus and minus two standard deviations of the mean and practically all (99.73 percent) of the area under the normal curve is within three standard deviations of the mean. Ii) The total area under the normal curve is 1. Iii) The mean of a normal probability distribution is 500 and the standard deviation is 10. About 68 percent of the observations lie between 480 and 520.

Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years, (based on data from "Getting Things Fixed," Consumer Reports). -The z-score of the student from section 2 is______ .

The driver's seat in most vehicles is set to comfortably fit a person who is at least 159 cm tall. The distribution of heights of adult women is approximately normal with a mean of 161.5 cm and a standard deviation of 6.3 cm. Determine the percentage of women who can be expected to be uncomfortable in the driver's seat of their car without some sort of an adjustment.

A national manufacturer of unattached garages discovered that the distribution of the lengths of time it takes two construction workers to erect the Red Barn model is approximately normally distributed with a mean of 32 hours and a standard deviation of 2 hours. What percent of the garages take between 32 and 34 hours to erect?

What is the value of the continuity correction factor?