Exam 6: The Normal Probability Distribution

Annual Rainfall Narrative The annual rainfall in a particular area of the country is normally distributed, with mean 100 cm and standard deviation 20 cm. -Refer to Annual Rainfall Narrative. A drought is said to occur after a year in which the annual rainfall dips below the 20th percentile. For a year to be classified as a year of drought, what would the annual rainfall in this area of the country have to be?

A television set manufacturer has found the length of time until the first repair is normally distributed, with a mean of 4.5 years and a standard deviation of 1.5 years. If the manufacturer wants only 10.2% of the first repairs to occur within the warranty period, how long should the warranty be?

For a continuous random variable x, P(6 < x < 8) is represented by the area under the probability function over the interval from 6 to 8, including both end points.

Salmon Flies Lifespan The lifetime of salmon flies is normally distributed, with a mean of 60 days and a standard deviation of 20 days. -Refer to Salmon Flies Lifespan paragraph. What percentage of salmon flies live fewer than 12 days?

The scores on an aptitude test are normally distributed with an unknown mean, a variance of 36, and only 7% of the scores below 26. What is the mean score?

If x is a normal random variable with mean = 4 and standard deviation = 2, and Y is a normal random variable with mean = 10 and standard deviation = 5, then P(x < 0) = P(Y < 0).

A normal random variable x has an unknown mean and standard deviation. The probability that x exceeds 4 is 0.975, and the probability that x exceeds 5 is 0.95. Find and

Suppose z has a standard normal distribution. Then between which two z-values (symmetrically distributed around the mean) would 95.96% of the possible z-values occur?

A chemical manufacturer sells its product in steel drums. The net weight of the chemical in the drums has a normal distribution with mean 145 kg and standard deviation 2 kg. The manufacturer guarantees its customers each drum will contain at least 140 kg of the chemical. What percentage of the drums will satisfy this guarantee?

The probability density function of a uniform random variable is an example of a normal distribution with a large population standard deviation.

National Achievement Test Scores Narrative The scores on a national achievement test were normally distributed, with a mean of 550 and a standard deviation of 112. -Refer to National Achievement Test Scores Narrative. If you achieved a score of 690, how far, in standard deviations, did your score depart from the mean?

Consider a binomial random variable x with n = 25 and p = 0.01. Would the normal approximation be appropriate here? Why or why not?

Let be a z-score that is unknown but identifiable by position and area. If the symmetrical area between - and + is 0.9544, the value of is 2.0.

Which of the following statements best describes continuous random variables?

Salmon Flies Lifespan The lifetime of salmon flies is normally distributed, with a mean of 60 days and a standard deviation of 20 days. -Refer to Salmon Flies Lifespan paragraph. What percentage of salmon flies live between 80 and 101 days?

Suppose the records of a motel show that, on average, 10% of prospective guests will not claim their reservation. If the motel accepts 218 reservations and there are only 200 rooms in the motel, what is the probability that all guests who arrive to claim a room will receive one?

Suppose z has a standard normal distribution. Then between which two z-values (symmetrically distributed around the mean) would 59.9% of the possible z-values occur?

For the standard normal distribution, find the value satisfying each of the following conditions. a. P(- $\lt$ z $\lt$ ) = 0.966 b. P(z < ) = 0.0174 c. P(z < ) = 0.5398

The distribution of final exam scores in an inferential statistics class is normal, with standard deviation 6. Find the mean score if 93.32% of the students received scores no higher than 90.

Members of the normal probability distribution family differ from one another only by which of the following measures?