Test 3 Practice

(6.1) Random samples of size 225 are drawn from a population with mean 100 and standard deviation 20. Find the mean and standard deviation of the sample mean.

?x? = 100, ?x? = 1.33

(6.1) A population has mean 75 and standard deviation 12.
a. ) Random samples of size 121 are taken. Find the mean and standard deviation of the sample mean.
b. ) How would the answers to part (a) change if the size of the samples were 400 instead of 121?

a. ) ?x? = 75, ?x? = 1.09
b. ) ?x? stays the same but ?x? decreases to 0.6

(6.2) A population has mean 128 and standard deviation 22.
a. ) Find the mean and standard deviation of for samples of size 36.
b. ) Find the probability that the mean of a sample of size 36 will be within 10 units of the population mean, that is, between

a. ) ?x? = 128, ?x? = 3.67
b. ) 0.9936

(6.2) A population has mean 73.5 and standard deviation 2.5.
a. ) Find the mean and standard deviation of for samples of size 30.
b.) Find the probability that the mean of a sample of size 30 will be less than 72.

a. ) ?x? = 73.5, ?x? = 0.456
b. ) 0.0005

(6.2) A normally distributed population has mean 25.6 and standard deviation 3.3.
a. ) Find the probability that a single randomly selected element X of the population exceeds 30.
b. ) Find the mean and standard deviation of for samples of size 9.
c.) Fin

a. ) 0.0918
b. ) ?x? = 25.6, ?x? = 1.1
c.) 0.0000

(6.2) A population has mean 557 and standard deviation 35.
a. ) Find the mean and standard deviation of for samples of size 50.
b. ) Find the probability that the mean of a sample of size 50 will be more than 570.

a. ) ?x? = 557, ?x? = 4.9494
b. ) 0.0043

(6.2) A normally distributed population has mean 1,214 and standard deviation 122.
a. ) Find the probability that a single randomly selected element X of the population is between 1,100 and 1,300.
b. ) Find the mean and standard deviation of for samples o

a. ) 0.5818
b. ) ?x? = 1214, ?x? = 24.4
c. ) 0.9998

(6.2) A population has mean 72 and standard deviation 6.
a. ) Find the mean and standard deviation of for samples of size 45.
b. ) Find the probability that the mean of a sample of size 45 will differ from the population mean 72 by at least 2 units, that

?x? = 72, ?x? = 0.8944
b. ) 0.0250

(6.2) Suppose the mean number of days to germination of a variety of seed is 22, with standard deviation 2.3 days. Find the probability that the mean germination time of a sample of 160 seeds will be within 0.5 day of the population mean.

0.9940

(6.2) Suppose the mean amount of cholesterol in eggs labeled "large" is 186 milligrams, with standard deviation 7 milligrams. Find the probability that the mean amount of cholesterol in a sample of 144 eggs will be within 2 milligrams of the population me

0.9994

(6.2) Suppose speeds of vehicles on a particular stretch of roadway are normally distributed with mean 36.6 mph and standard deviation 1.7 mph.
a. ) Find the probability that the speed X of a randomly selected vehicle is between 35 and 40 mph.
b. ) Find t

a. ) 0.8036
b. ) 1.0000

(6.2) Suppose the mean cost across the country of a 30-day supply of a generic drug is $46.58, with standard deviation $4.84. Find the probability that the mean of a sample of 100 prices of 30-day supplies of this drug will be between $45 and $50.

0.9994

(6.2) Scores on a common final exam in a large enrollment, multiple-section freshman course are normally distributed with mean 72.7 and standard deviation 13.1.
a. ) Find the probability that the score X on a randomly selected exam paper is between 70 and

a. ) 0.2955
b. ) 0.8977

(6.2) Suppose that in a certain region of the country the mean duration of first marriages that end in divorce is 7.8 years, standard deviation 1.2 years. Find the probability that in a sample of 75 divorces, the mean age of the marriages is at most 8 yea

0.9251

(6.2) A high-speed packing machine can be set to deliver between 11 and 13 ounces of a liquid. For any delivery setting in this range the amount delivered is normally distributed with mean some amount ? and with standard deviation 0.08 ounce. To calibrate

0.9982

(6.3) The proportion of a population with a characteristic of interest is p = 0.37. Find the mean and standard deviation of the sample proportion p? obtained from random samples of size 1,600.

...

(6.3) The proportion of a population with a characteristic of interest is p = 0.76. Find the mean and standard deviation of the sample proportion p? obtained from random samples of size 1,200.

...

(6.3) Random samples of size 225 are drawn from a population in which the proportion with the characteristic of interest is 0.25. Decide whether or not the sample size is large enough to assume that the sample proportion p? is normally distributed.

...

(6.3) Random samples of size n produced sample proportions p? as shown. In each case decide whether or not the sample size is large enough to assume that the sample proportion p? is normally distributed.
a. ) n = 50, p? = 0.48
b. ) n = 50, p? = 0.12
c. )

...

(6.3) A random sample of size 121 is taken from a population in which the proportion with the characteristic of interest is p = 0.47. Find the indicated probabilities.
a. ) P(0.45

...