1. Given that X is a continuous random variable that has a uniform probability distribution, and 0 < X < 8:

a. Calculate P(X < 4) (to 3 significant digits). P(X<4)=(<4)=

b. Determine the mean () and standard deviation () of the distribution (to 3 significant digits). ==

==

2. Calculate the margin of error and construct the confidence interval for the population mean using the Student's t-distribution (you may assume the population data is normally distributed).

T-Distribution Table

a. x=88.2,n=69,s=15.3,x=88.2,=69,=15.3, 90% confidence

E==

Round to two decimal places if necessary

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Round to two decimal places if necessary

b. x=37.2,n=43,s=12.1,x=37.2,=43,=12.1, 95% confidence

E==

Round to two decimal places if necessary

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Round to two decimal places if necessary

3. A health insurance broker records the monthly extended health and dental insurance premiums for 18 non-smoking white-collar clients between the ages of 31 and 40 (measured in $):

125	108	82	101	92	112	103	108	90
119	64	97	71	48	105	71	127	148

T-Distribution Table

a. Calculate the sample mean and standard deviation.

x=x=

Round to the nearest cent

s==

Round to the nearest cent

b. Construct a 98% confidence interval for the mean monthly insurance premium for all non-smoking white-collar clients between the ages of 31 and 40.

<<<<

Round to the nearest cent

4. Calculate the indicated probabilities, assuming that Z is a continuous random variable that follows a standard normal distribution: Standard Normal Distribution Table

a. P(Z<2.63)=(<2.63)=

b. P(Z>3.06)=(>3.06)=

c. P(2.25

5. If it is appropriate to do so, use the normal approximation to the p^^-distribution to calculate the indicated probability:

Standard Normal Distribution Table

n=120,p=0.364=120,=0.364 P(0.35

Enter 0 if it is not appropriate to do so.