ORMS 3310 Module 6

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is between -2.89 and -1.03 is ________.

0.1496

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. So 50% of the possible Z values are between ________ and ________ (symmetrically distributed about the mean).

-0.67 and 0.67 or -0.68 and 0.68

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 30) 1. So 96% of the possible Z values are between ________ and ________ (symmetrically distributed about the mean).

-2.05 and 2.05 or -2.06 and 2.06

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is less than -2.20 is ________.

0.0139

A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68years and a standard deviation of 3.5 years. What proportion of the plan recipients would receive payments beyond age 75?

0.0228

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is more than 0.77 is ________.

0.2206

The probability that a standard normal variable Z is positive is ________.

0.50

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is between -0.88 and 2.29 is ________.

0.7996

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is more than -0.98 is ________.

0.8365

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is less than 1.15 is ________.

0.8749

Given that X is a normally distributed variable with a mean of 50 and a standard deviation of 2, find the probability that X is between 47 and 54.

0.9104 (54-50/2) , (47-50/2) P = 2 , P= -1.5 0.9772 - 0.0668 = .9104

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is between -2.33 and 2.33 is ________.

0.9802

The owner of a fish market determined that the mean weight for a catfish is 3.2 pounds. He also knew that the probability of a randomly selected catfish that would weigh more than3.8 pounds is 20% and the probability that a randomly selected catfish that would weigh less than 2.8 pounds is 30%. The middle 40% of the catfish will weigh between ______ pounds and ______ pounds.

2.8 and 3.6

The owner of a fish market determined that the mean weight for a catfish is 3.2 pounds. He also knew that the probability of a randomly selected catfish that would weigh more than 3.8 pounds is 20% and the probability that a randomly selected catfish that would weigh less than 2.8 pounds is 30%. The probability that a randomly selected catfish will weigh between 2.6 and 3.6 pounds is ______.

50% or 0.5

A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68years and a standard deviation of 3.5 years. Find the age at which payments have ceased for approximately 86% of the plan participants.

71.78 years old

If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes.

A) 0.3085

For some value of Z, the value of the cumulative standardized normal distribution is 0.8340. The value of Z is

A) 0.97

The value of the cumulative standardized normal distribution at Z is 0.8770. The value of Z is

A) 1.16

Which of the following about the normal distribution is not true?

A) It is a discrete probability distribution.

True or False: Any set of normally distributed data can be transformed to its standardized form.

A) True

True or False: The probability that a standard normal variable, Z, falls between -1.50 and 0.81 is 0.7242.

A) True

True or False: The probability that a standard normal variable, Z, is between 1.00 and 3.00 is 0.1574.

A) True

True or False: The probability that a standard normal variable, Z, is between 1.50 and 2.10 is the same as the probability Z is between -2.10 and -1.50.

A) True

True or False: Theoretically, the mean, median, and the mode are all equal for a normal distribution.

A) True

For some value of Z, the value of the cumulative standardized normal distribution is 0.2090. The value of Z is

B) -0.81

The value of the cumulative standardized normal distribution at Z is 0.6255. The value of Z is

B) 0.32

If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, 75.8% of the college students will take more than how many minutes when trying to find a parking spot in the library parking lot?

B) 2.8 minutes

True or False: The "middle spread," that is the middle 50% of the normal distribution, is equal to one standard deviation.

B) False

True or False: The probability that a standard normal variable, Z, falls between -2.00 and -0.44 is 0.6472.

B) False

True or False: The probability that a standard normal variable, Z, is below 1.96 is 0.4750.

B) False

True or False: The probability that a standard normal variable, Z, is less than 5.0 is approximately 0.

B) False

The value of the cumulative standardized normal distribution at 1.5X is 0.9332. The value of X is

C) 1.00

In its standardized form, the normal distribution

C) has a mean of 0 and a standard deviation of 1.

If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will take between 2 and 4.5minutes to find a parking spot in the library parking lot.

D) 0.7745

If a particular set of data is approximately normally distributed, we would find that approximately

D) All the above. A) 4 of every 5 observations would fall between ±1.28 standard deviations around the mean. B) 19 of every 20 observations would fall between ±2 standard deviations around the mean. C) 2 of every 3 observations would fall between ±1 standard deviation around the mean.