Sta 120 Sp 04 Inst: Wong, D

Math 227 Sp’08 Inst: Wong, D. Ch5 to 6 Test Name: ______

#1 For the following probability distribution,

x 1 2 3 4 P(x) 0.25 0.10 0.5

4pt. (a) Find P( x = 3).

10pt. (c) Find the mean and standard deviation of the distribution.

#2 A researcher from a college reported that 72% of single-vehicle traffic fatalities 6pt. that occur at night on weekends involve an intoxicated driver. If a sample of 15 single-vehicle traffic fatalities that occur at night on a weekend is selected, use the Binomial formula to find the probability that exactly 12 involve a driver who is intoxicated.

#3 If 60% of all women are employed outside the home, use the Binomial table to 6pt. find the probability that in a sample of 20 women at least 16 are employed outside of the home. #4 A lottery offers one $1000 prize, one $500 prize, and five $100 prizes. One 8pt. thousand tickets are sold at $3 each. Find the expectation (E(x)) if a person buys one ticket.

#5 Assume the z scores are normally distributed with a mean of 0 and a standard deviation of 1. 4pt. a) Find P(z > -1.58)

4pt. b) Find P( -2.85 < z < -1.07)

#6 Determine the value of z so that the area under the standard normal curve to 5pt. the left of z is 0.0250.

#7 IQ scores are normally distributed with a mean of 100 and a standard deviation 8pt. of 15. If we define a genius to be someone in the top 1% of IQ scores, find the score separating geniuses from the rest of us. #8 Heights of women are normally distributed with a mean of 63.6 in. and a standard deviation of 2.5 in. (based on data from the National Health Survey). 10pt. If a woman is randomly selected, find the probability that her height is between 60 in. and 69 in.

#9 Replacement times for TV sets have a mean of 8.2 years and a standard deviation of 1.4 years. If 45 TV sets are randomly selected, 4pt. a) should the mean replacement time, x , be normally distributed? Explain.

10pt. b) find the probability that x will be greater than 17.2 years. #10 A history class has 75 students. If there is a 18% absentee rate per class meeting,

4pt. (a) find the mean and standard deviation of the number of students who will be absent per class meeting.

9pt. (b) use a normal distribution to approximate a binomial distribution procedure to find the probability that among 75 students, there are at most 15 students who will be absent per class meeting.

#11 True or False 2pt. each ______a) If x is a random variable for a binomial distribution, x is a discrete random variable.

______b) If the population distribution is normally distributed and a sample size of 20 is randomly selected from the population, the distribution of the sampling mean x is not guaranteed to be normally distributed.

______c) As n increases,  x decreases.

______d) For the standard normal distribution  = 0 and  = 1.