1) A population has parameters

=

168.5

=168.5

and

=

87.9

=87.9

. You intend to draw a random sample of sizen

=

85

n=85

.

What is the mean of the distribution of sample means?

x

=

x=

What is the standard deviation of the distribution of sample means?

(Report answer accurate to 2 decimal places.)

x

=

x=

2) A population of values has a normal distribution with

=

155.2

=155.2

and

=

36

=36

. You intend to draw a random sample of sizen

=

14

n=14

.

Find the probability that a single randomly selected value is less than 186.

P(X< 186) =

Find the probability that a sample of sizen

=

14

n=14

is randomly selected with a mean less than 186.

P(M< 186) =

Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exactz-scores orz-scores rounded to 3 decimal places are accepted.

3)The lengths of pregnancies in a small rural village are normally distributed with a mean of 268 days and a standard deviation of 13 days.

In what range would you expect to find the middle 98% of most pregnancies?

Betweenand.

If you were to draw samples of size 32 from this population, in what range would you expect to find the middle 98% of most averages for the lengths of pregnancies in the sample?

Betweenand.

Enter your answers as numbers. Your answers should be accurate to 1 decimal places.

4)Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 7.1-in and a standard deviation of 1.2-in.

In what range would you expect to find the middle 95% of most head breadths?

Betweenand.

If you were to draw samples of size 34 from this population, in what range would you expect to find the middle 95% of most averages for the breadths of male heads in the sample?

Betweenand.

Enter your answers as numbers. Your answers should be accurate to 2 decimal places

5)A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 242.9-cm and a standard deviation of 0.7-cm. For shipment, 12 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is less than 243.2-cm.

P(M< 243.2-cm) =

Enter your answer as a number accurate to 4 decimal places. Answers obtained using exactz-scores orz-scores rounded to 3 decimal places are accepted.

6)You measure 26 dogs' weights, and find they have a mean weight of 68 ounces. Assume the population standard deviation is 10.8 ounces. Based on this, construct a 90% confidence interval for the true population mean dog weight.

Give your answers as decimals, to two places

ounces

7)Assume that a sample is used to estimate a population mean

. Find the margin of errorM.E.that corresponds to a sample of size 7 with a mean of 59.9 and a standard deviation of 11.8 at a confidence level of 80%.

Report ME accurate to one decimal place because the sample statistics are presented with this accuracy.

M.E.=

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.