A manufacturer claims that the replacement time for their CD players has a mean of 7 years and a standard deviation of 1.4 years. If this is true, find the probability that a) one randomly selected CD player is replaced in 6.2 years or less b) in a random sample of 30 CD players, the mean replacement time is 6.2 years or less c) In part b), are the assumptions of the Central Limit Theorem satisfied?  Explain

The number of babies in a litter of rabbits is approximately Poisson distribution with mean 6. Litters can occur once per month for a 9 month period (3 months infertile). What is the standard deviation of the number of babies in one litter? What is the probability of a litter with exactly one rabbit? What is the approximate probability that over a 9 month period, a rabbit will have more than 65 babies (use the Central Limit Theorem, continuity correction is optional)? Incidentally, the plot at right shows the exact Poissondistribution you’ll be using, and you’ll note it looks quite a bit like some other distribution . .

A hospital receives a pharmaceutical delivery each morning at a time that varies uniformly between 7:00 AM and 8:00 AM. Please show work. a)  Find the probability that the delivery on a given morning will occur between 7:15 AM and 7:30 AM. b)  What is the expected time and variance of the delivery time? c)  Find the probability that the time of delivery will be within 1 standard deviation of the expected time,i.e.P(X X X X X ).

The length of time it takes customers of a payday lender to repay their loan has a mean of 18 days and a standard deviation of 5 days . For a random sample of 40 borrowers , what is the probability that their mean payback time will be: i.) under 17 days  ii.) over 20 days iii.) Between 17 and 20 days  Please provide worked out solution in excel    thank you in advance

The ages of workers in the Illuminex plant are approximately normally distributed, with a mean of 45 years and a standard deviation of 12 years.  A worker is stopped at random and asked to fill out a questionnaire.  What is the probability that this worker is a) less than 30 years old?b) between 35 and 55 years old?c)  more than 60 years old?