Questions:

1. The probability that a standard normal variable between 0 and 21 is 0.4292. Find z1. 2. The probability that a standard normal variable is above a positive value of 21 is 0.1230. Find the value of z1. 3. For some positive value of z1, the probability that a standard normal variable is between 21 and - 1.5 is 0.5396. Find the value of z1. 4. According to an intern report, the mean monthly pay for interns at Facebook is $6058 and the standard deviation is $500. Suppose that the intern monthly pay is normally distributed. Answer the following questions. a. What is the probability that the monthly pay of an intern at Facebook is less than $5900? b. What is the probability that the monthly pay of an intern at Facebook is between $5700 and $6100? c. What is the probability that the monthly pay of an intern at Facebook is above $6500? d. Ninety-five percent of the intern monthly pays are between what two values, symmetrically distributed around the mean? 5. A student scored 70 on a standardised test and was told that 33% of scores were lower than his. If test scores were normally distributed with a standard deviation of 20, what was the mean score on the test? 6. The diameter of pipes supplied by a manufacturer varies but is normally distributed. Mean diameter is 10cm, and the probability that a pipe with a diameter exceeding 11cm is 0.1587. What is the standard deviation of diameters?7. A study of the time spent shopping in a supermarket for a market basket of 20 specific items showed an approximately uniform distribution between 20 minutes and 40 minutes. What is the probability that the shopping time will be a. Between 25 and 30 minutes? b. Less than 35 minutes? c. What are the mean and standard deviation of the shopping time