Exam 6: The Normal Probability Distribution

The net profit from a certain investment is normally distributed with a mean of $10,000 and a standard deviation of $5,000. The probability that the investor will not have a net loss is:

Determine the z-score associated with an area of 0.25 from the mean of a normal distribution to that positive z-score.

A loaf of bread is normally distributed with a mean of 22 ounces and a standard deviation of ½ ounces. -The probability that a loaf of bread is < 24 ounces is ______.

i. The uniform probability distribution's standard deviation is proportional to the distribution's range. ii. The uniform probability distribution is symmetric about the mode. iii. For a uniform probability distribution, the probability of any event is equal to 1/(b-a).

Normally distributed observations such as a person's weight, height or shoe size occur quite frequently in nature. Business people who are aware of this use it to their advantage. A purchasing agent for a large retailer buying 15,000 pairs of women's shoes used the normal curve to decide on the order quantities for the various sizes. If women's average shoe size is 7.5 with a standard deviation of 1.5, ______pairs should be ordered between sizes 6.5 and 9?

A new extended-life light bulb has an average service life of 750 hours, with a standard deviation of 50 hours. If the service life of these light bulbs approximates a normal distribution, about what percent of the distribution will be between 600 hours and 900 hours?

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). -Assume that human body temperatures are normally distributed with a mean of 36.4°C and a standard deviation of 0.7°C. If we define a fever to be a body temperature above 38.0°C_____, percentage of normal and healthy persons would be considered to have a fever. This percentage suggests that a cutoff of 38.0°C is ( (appropriate/inappropriate) )?

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 between $47,000 and $53,000?

Determine the z-score associated with an area of 0.48 from the mean of a normal distribution to that positive z-score.

Which of the following is true in a normal distribution?

A major credit card company has determined that customers charge between $100 and $1,100 per month. Given that the average monthly amount charged is uniformly distributed, what is the probability that a person charges less than $200 per month?

i. For any uniform probability distribution, the mean and standard deviation can be computed by knowing the maximum and minimum values of the random variable. Ii) In a uniform probability distribution, P(x) is constant between the distribution's minimum and maximum values. Iii) The uniform probability distribution's shape is a rectangle.

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 an "A" on the test, a student must be in the top 5% of the class. What should a student score to receive an "A"?

Tables of normal distribution probabilities are found in many statistics books. These probabilities are calculated from a normal distribution with

The standardized z value measures distance from the mean in units of__________ .

A financial advising company has determined that the price-to-earnings ratios for 20 randomly selected publicly traded companies range between 0.9 and 2.9. Given that the price-to-earnings ratios are uniformly distributed, what is the average price-to-earnings ratio?

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 standard deviation for this distribution?

i. A continuity correction compensates for estimating a discrete distribution with a continuous distribution. Ii) The normal probability distribution is generally deemed a good approximation for the binomial probability distribution when np and n(1 - p) are both greater than five. Iii) When a continuity correction factor is used, its value is 1.

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 mean for this distribution?

Two competitive brothers, who work in two different industries, were comparing their salaries. Because there is a difference of 4 years in their respective work experience, they decided to compare, not their actual salaries, but to compare their salaries against their company averages to see who is doing better. The following gives the brothers' salaries, companies' mean, and standard deviation for each company. What is the z-score of Tom's salary?