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Exam 8: Continuous Probability Distributions

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Question 51

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Given that Z is a standard normal random variable, a positive z value means that:

A) the value $z$ is to the left of the mean.
B) the value $z$ is to the right of the median.
C) the $z$ value is to the right of the mean.
D) both B and C are correct.

E) B) and D)
F) A) and C)

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Question 52

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In the standard normal distribution, z_0.05 = 1.645 means that there is a 5% chance that the standard normal random variable Z assumes a value above 1.645.

A) True
B) False

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Question 53

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Given that Z is a standard normal variable, the variance of Z:

Using the standard normal curve, the probability or area between z = -1.28 and z = 1.28 is 0.1003

For a normal curve, if the mean is 25 minutes and the standard deviation is 5 minutes, the area to the right of 25 minutes is 0.50.

The weights of cans of soup produced by a company are normally distributed, with a mean of 150 g and a standard deviation of 5 g. a. What is the probability that a can of soup selected randomly from the entire production will weigh less than 143 g? b. Determine the minimum weight of the heaviest 5% of all cans of soup produced. c. If 28 390 of the cans of soup of the entire production weigh at least 157.5 g, how many cans of soup have been produced?

What proportion of the data from a normal distribution is within 2 standard deviations of the mean?

The time required to complete a particular assembly operation is uniformly distributed between 12 and 18 minutes. a. What is the probability density function for this uniform distribution? b. What is the probability that the assembly operation will require more than 16 minutes to complete? c. Find the expected value and standard deviation for the assembly time.

If X is a normal random variable with a mean of 45 and a standard deviation of 8, find the following probabilities: a. P(X $\geq$ 50). b. P(X $\leq$ 32). c. P(37 $\leq$ X $\leq$ 48). d. P(50 $\leq$ X $\leq$ 60). e. P(X = 45).

The time it takes a technician to fix a computer problem is exponentially distributed, with a mean of 15 minutes. a. What is the probability density function for the time it takes a technician to fix a computer problem? b. What is the probability that it will take a technician less than 10 minutes to fix a computer problem? c. What is the variance of the time it takes a technician to fix a computer problem? d. What is the probability that it will take a technician between 10 to 15 minutes to fix a computer problem?

Which of the following distributions is considered the cornerstone distribution of statistical inference?

If Z is a standard normal random variable, find the value z for which: a. the area to the left of 0.0336. b. the area to the right of z is 0.0075is 0.1292. c. the area to the left of z is 0.0.9909.

A supermarket receives a delivery each morning at a time that varies uniformly between 5:00 and 7:00am. a. Find the probability that the delivery on a given morning will occur between 5:30 and 5:45am. b. What is the expected time of delivery? c. Determine the standard deviation of the delivery time. d. Find the probability that the time of delivery will be within half a standard deviation of the expected time.

Suppose that the probability p of a success on any trial of a binomial distribution equals 0.80. For which value of the number of trials, n, would the normal distribution provide a good approximation to the binomial distribution?

The time it takes a student to complete a 3-hour business statistics sample exam paper is uniformly distributed between 150 and 230 minutes. a. What is the probability density function for this uniform distribution? b. Find the probability that a student will take no more than 180 minutes to complete the sample exam paper. c. Find the probability that a student will take no less than 205 minutes to complete the sample exam paper. d. What is the expected amount of time it takes a student to complete the sample exam paper? e. What is the standard deviation for the amount of time it takes a student to complete the sample exam paper?

If X is a normal random variable with a mean of 78 and a standard deviation of 5, find the following probabilities: a. P(X ? 87). b. P(X ? 91). c. P( $\le$ X $\le$ ).

In the normal distribution, the curve is skewed.

The mean and standard deviation of a normally distributed random variable that has been standardised are one and zero, respectively.

The exponential distribution is suitable to model the length of time that elapses before the first telephone call is received by a switchboard.

If Z is a standard normal random variable, find the value of z that has the following probabilities: a. P(Z ≤ z) = 0.3228. b. P(Z ≥ z) = 0.8289.