Exam 6: The Normal Distribution and Other Continuous Distributions

TABLE 6-7 A company has 125 personal computers. The probability that any one of them will require repair on a given day is 0.15. -Referring to Table 6-7 and assuming that the number of computers that requires repair on a given day follows a binomial distribution, compute the probability that there will be less than 25 or more than 30 computers that require repair on a given day using a normal approximation.

The probability that a standard normal random variable, Z, falls between - 1.50 and 0.81 is 0.7242.

The true length of boards cut at a mill with a listed length of 10 feet is normally distributed with a mean of 123 inches and a standard deviation of 1 inch. What proportion of the boards will be over 125 inches in length?

The amount of pyridoxine (in grams) in a multiple vitamin is normally distributed with µ = 110 grams and a = 25 grams. What is the probability that a randomly selected vitamin will contain less than 100 grams or more than 120 grams of pyridoxine?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of The probability that Z values are larger than____ is 0.3483.

The probability that a standard normal random variable, Z, is between 1.50 and 2.10 is the same as the probability Z is between - 2.10 and - 1.50.

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of The probability that Z is less than -2.20 is____ .

TABLE 6-7 A company has 125 personal computers. The probability that any one of them will require repair on a given day is 0.15. -Referring to Table 6-7 and assuming that the number of computers that requires repair on a given day follows a binomial distribution, compute the probability that there will be less than 8 computers that require repair on a given day using a normal approximation.

TABLE 6-4 John has two jobs. For daytime work at a jewelry store he is paid $200 per month, plus a commission. His monthly commission is normally distributed with mean $600 and standard deviation $40. At night he works as a waiter, for which his monthly income is normally distributed with mean $100 and standard deviation $30. John's income levels from these two sources are independent of each other. -Referring to Table 6-4, find the mean and standard deviation of John's total income from these two jobs for a given month.

You were told that the mean score on a statistics exam is 75 with the scores normally distributed. In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. The middle 95.46% of the students will score between which two scores?

For some positive value of X, the probability that a standard normal variable is between 0 and +2X is 0.1255. What is the value of X?

TABLE 6-3 The number of column inches of classified advertisements appearing on Mondays in a certain daily newspaper is normally distributed with population mean 320 and population standard deviation 20 inches. -Referring to Table 6-3, for a randomly chosen Monday the probability is 0.1 that there will be less than how many column inches of classified advertisements?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of The probability that Z is more than -0.98 is______ .

The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. A citation catfish should be one of the top 2% in weight. Assuming the weights of catfish are normally distributed, at what weight (in pounds) should the citation designation be established?

Scientists in the Amazon are trying to find a cure for a deadly disease that is attacking the rain forests there. One of the variables that the scientists have been measuring involves the diameter of the trunk of the trees that have been affected by the disease. Scientists have calculated that the average diameter of the diseased trees is 42 centimeters. They also know that approximately 95% of the diameters fall between 32 and 52 centimeters and almost all of the diseased trees have diameters between 27 and 57 centimeters. When modeling the diameters of diseased trees, which distribution should the scientists use?

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 1 patient per hour. What is the probability that a randomly chosen arrival to be more than 2.5 hours?

The amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is_____ that a product is assembled in between 10 and 12 minutes.

Theoretically, the mean, median, and the mode are all equal for a normal distribution.

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of So 96% of the possible Z values are between ______ and ______ (symmetrically distributed about the mean).

The amount of pyridoxine (in grams) in a multiple vitamin is normally distributed with µ = 110 grams and a = 25 grams. What is the probability that a randomly selected vitamin will contain at least 100 grams of pyridoxine?