Question

1.A jar contains 3 pennies, 8 nickels and 6 dimes. A child selects 2 coins at random without replacement from the jar. Let X represent the amount in cents of the selected coins.

Find the probability X = 10.     

Find the probability X = 11.     

Find the expected value of X.

2.Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1.

If P(z>d)=0.9434P(z>d)=0.9434, find d.

3.A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 233.9-cm and a standard deviation of 0.9-cm. For shipment, 25 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is between 233.7-cm and 234.3-cm.
P(233.7-cm < M < 234.3-cm) =

4.

Data were collected from a survey given to graduating college seniors on the number of times they had changed majors. From that data, a probability distribution was constructed. The random variable X is defined as the number of times a graduating senior changed majors. It is shown below:

xx	0	1	2	3	4	5	6	7	8
P(X=x)P(X=x)	0.226	0.212	0.234	0.193	0.089	0.03	0.013	0.002	0.001

1. What is the probability that a randomly selected student changed his or her major at least once?
       
   
2. What is the probability that a randomly selected student changed his or her major at most twice?
       
   
3. Given that a randomly selected person did change majors, what is the probability that he or she changed majors more than three times?
     

Answer 1