Discuss the below:
Q1. A file cabinet manufacturer estimates that 5% of its file cabinets will have drawers that close improperly. Assume a production run of 120 cabinets is completed.
a. What is the mean and standard deviation of this distribution?
b. What is the probability that 7 or more are defective?
c. What is the probability that exactly 7 cabinets are defective?
d. What is the probability that there are more than 8 defective file cabinets?
Q2. A clothing store asserts that 60% of its customers pay by credit. On a particular day, 35 customers purchased items at the store.
a. What is the mean and standard deviation of the binomial distribution?
b. What is the probability that half (18 or more) of the customers paid by credit?
c. What is the probability that 30 or more paid by credit?
d. What is the probability that less than 12 paid by credit?
e. What is the probability that 12 to 30 paid by credit?
Q3. It is very difficult for small businesses to be successful. The Small Business Administration estimates that 20 percent will dissolve or go bankrupt within two years. A sample of 50 new businesses is selected.
a. What is the mean and standard deviation of this distribution?
b. What is the probability that more than 16 in the sample will go bankrupt?
c. What is the probability that exactly 14 will go bankrupt?
d. What is the probability that between 7 and 9 businesses will go bankrupt?
e. What is the probability that between 7 and 15 businesses will go bankrupt?