# MAT540: Statistics

Find the standardized variable Z if X has

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Mean 16 and standard deviation 7.

Z = (X – ) /

Find the standardized variable Z if X has

Mean 58 and standard deviation 9.

Z = (X – ) /

Find the standardized variable Z if X has

Mean 151 and variance 4.

Z = (X – ) /

Find the area under the standard normal curve to the right of

z = -0.95

P [Z > -0.95] =

the absolute tolerance is +/-0.0001

Find the area under the standard normal curve to the right of:

z = 0.40

P [Z > 0.40] =

the absolute tolerance is +/-0.0001

Find the area under the standard normal curve over the interval z = −0.59 to z = 0.59. Compute probabilities using the standard normal table in Appendix B (Table 3). Round the answer to four decimal places.

Area = .

the absolute tolerance is +/-0.0015

Find the area under the standard normal curve over the interval z = 0.36 to z = 2.29. Compute probabilities using the standard normal table in Appendix B (Table 3). Round the answer to four decimal places.

Area = .

the absolute tolerance is +/-0.0001

For a standard normal random variable Z, find P[− 1.6 < z < 2.21]. Compute probabilities using the standard normal table in Appendix B (Table 3). Round the answer to four decimal places.

P[− 1.6 < z < 2.21] = .

Scores on a certain nationwide college entrance examination follow a normal distribution with a mean of 450 and a standard deviation of 100. Find the probability that a student will score:

Over 570.0.

the absolute tolerance is +/-0.0001

Scores on a certain nationwide college entrance examination follow a normal distribution with a mean of 600 and a standard deviation of 100. Find the probability that a student will score:

Between 450 and 740.0.

the absolute tolerance is +/-0.0001

 A population has mean 58 and standard deviation 17. Calculate   for a random sample of size 14.

A population has mean 62 and standard deviation 14. Calculate   for a random sample of size 5.   (Round to one decimal place.)

A population has standard deviation 7. What is the standard deviation of   for a random sample of size   (Round to one decimal place.)

A population has standard deviation 6. What is the standard deviation of   for a random sample of size   (Round to one decimal place.)

Suppose the weights of packages of lettuce coming off a packaging line have a normal distribution with mean 8.7 ounces and standard deviation 0.2 ounce. If every package is labeled 8.3 ounces, what proportion of the packages weigh less than the labeled amount? % (Round to the whole.)

Suppose the weights of the contents of cans of mixed nuts have a normal distribution with mean 32.8 ounces and standard deviation 0.4 ounce.

If two packages are randomly selected, what is the probability that the average weight is less than 32 ounces?

Round to one decimal place.

the tolerance is +/-2%

The number of complaints per day, X, received by a cable TV distributor has the probability distribution

 X 0 1 2 3 f(X) 0.2 0.3 0.1 0.4

Find the expected number of complaints per day.

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