Practice problems:

Consider a randomly selected group of 100 students. Suppose 40 students are majoring in biology or chemistry. Suppose 15 students major chemistry. Assume that 5 students are majoring both biology and chemistry. If a student is selected randomly,

1. a) what is the probability that the student is from other majors?
2. b) what is the probability that the selected student majors only in chemistry?
3. c) what is the probability that the selected student is a biology major?
4. d) If the sleeted student is not a chemistry major, what is the probability that the student is a biology major?

Consider a drive-through restaurant. The restaurant experiences, on average, 30%

customers use visa cards. Consider a random sample of 20 customers.

a) What is the probability that at least 5 will use visa cards?

b) What is the probability that more than 15 or less than 10 customers will use visa cards?

Consider the cumulative distribution function of a random variable Y, F(y)=cy2; 0

a) Compute the constant c.

b) What is the probability that Y is at most 1?

c) What is the expected value of Y?

d) Calculate the median of Y.

The following data shows the gas mileage (miles per gallon) of a car sample of a particular brand of car.

20.221.325.022.523.922.822.524.224.623.9

27.422.222.0720.324.221.623.220.119.625.4

a) Construct 90% confidence interval for the population mean, and interpret the confidence interval.

b) The car manufacturer claims that the average gas mileage of this brand of car is 20 miles per gallon. Does the data support the above claim? Conduct a test using the level of significance 0.01.

Consider the data given in question #4.

a) Compute the sample mean and the standard deviation of the data.

b) What proportion of the data is three standard deviation of the mean value?

c) Calculate the first and the third quartiles of the data. Show your work.

d) Calculate the Z-score of 19.6 and interpret the Z-score value.