Exam 6: Continuous Probability Distributions

A loaf of bread is normally distributed with a mean of 22 ounces and a standard deviation of ½ ounces. (i) The probability that a loaf of bread is < 20 ounces is 0.0. (ii. The probability that a loaf of bread is > 21 ounces is 0.4772. (iii) The probability that a loaf of bread is < 24 ounces is 1.0.

For the standard normal distribution, what z-score corresponds with the 85% percentile?

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?

The shape of any uniform probability distribution is

What is the proportion of the total area under the normal curve within plus and minus two standard deviations of the mean?

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. (i) 250 students earned more than $30,000. (ii. 500 students earned between $20,000 and $40,000. (iii) 3 students earned less than $22,500.

(i. The proportion of the area under a normal curve to the right of z = -1.21 is 0.8869. (ii) The proportion of the area under a normal curve to the left of z = 0.50 is 0.6915. (iii) The proportion of the area under a normal curve to the left of z = -2.10 is 0.0179.

(i. About 95.5% percent of the area under the normal curve is within plus three and minus three standard deviations of the mean. (ii) The normal distribution is a continuous probability distribution. (iii) In a standard normal distribution, µ = 0 and $\sigma$ = 1.

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.

(i. About 95.5% percent of the area under the normal curve is within plus one and minus one standard deviation of the mean. (ii) The normal distribution is a continuous probability distribution. (iii) In a standard normal distribution µ = 0 and $\sigma$ = 1.

What is the distribution with a mean of 0 and a standard deviation of 1 called?

A loaf of bread is normally distributed with a mean of 22 ounces and a standard deviation of ½ ounce. (i) The probability that a loaf of bread is between 20.75 and 23.25 ounces is 0.7662. (ii. The probability that a loaf of bread is > 21 ounces is 0.9772.

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

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 "C" on the test, a student must be in the top 25% of the class. What should a student score to receive a "C"?

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. (i) the probability of a pregnancy lasting 300 days or longer is 0.0166. (ii. The result suggests that the husband is the father of the child.

Determine the z-score associated with an area of 0.4925 from the mean of a normal distribution to that negative z-score.

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?

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). (i) If you want to provide a warranty so that only 3% of the TV sets will be replaced before the warranty expires, the length of warranty you would recommend would be 6.13 years. (ii. The probability that a randomly selected TV will be replaced after more than 10.0 years is 0.0505.

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?

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"?