1) A valid PDF has the following distribution: p(x)=0.075x + 0.2, where 3

What is the S.D. of the random variable, X?

(If needed, please round your answer to the nearest 4th digit after decimal place.)

2) The weights of 3-month-old babies are normally distributedbaby boys with a mean of13.7pounds and a standard deviation of1.62,and baby girls with a mean of13.1pounds and a standard deviation of1.64.

Would it be unusual to find a 3-month-old baby girl who weighed more than 15 pounds?

3) The thickness in micronsof a protective coating applied to a conductor designed to work in corrosive conditions is uniformly distributed on the interval from15to40.

What is the probability that the thickness of the coating is between 35 and 45 microns?

4) A random sample of 50 CMU students were asked how many hours they spend surfing on the internet per week. The result showed a sample mean of 27.25 hours with a standard deviation of 5.5 hours. Estimate the population mean (hours spend surfing on the internet per week) at the 90% level of confidence.

Find the margin of error.

5) Record shows that the mean IQ score for college students was 115 with a S.D. of 13. Dr. Fu wants to evaluate the IQ scores of students in CMU. If he wants to limit the error within 1 points from the mean, what sample size he will need so he will have 96% of confidence in his conclusion?

6) A geologist studying the movement of the earth's crust at a particular location on California's San Andreas fault found many fractures in the local rock structure. In an attempt to determine the mean angle of the breaks, she sampled 60 fractures and found the sample mean and standard deviation to be 39.5 and 17.1 degrees, respectively. To estimate the mean angular direction of the fractures at a confidence level of 98%, what is the margin of error of the estimation?

7) The Chevrolet Boltcars were reviewed to have an EPA rating of 238 miles between battery charges. To test this claim, Dr. Fu use a n=36 road tests and that the average miles between charges was244 miles with a standard deviation of 19.2 miles.

Compute the right boundary of a 91% confidence interval for the population average miles between battery charges.

8) According to the record, 58% of the population in Mt Pleasant are males. Dr. Fu wants to use a random sample to verify the number. If he wants to limit the error within 8 percent from the mean, at 91% C.L., what sample size is needed?

9) A record shows that the proportion of sports utility vehicles (SUVs) being driven in a country was 0.1. Dr. Fu conducted a survey this year to estimate the proportion of SUVs in this country. A random sample of 450 registrations are selected from a Department of Motor Vehicles database, and 39 are classified as SUVs.

Compute the left boundary of a 96% confidence interval for the proportion estimation.