Sales for Hobi-cat, a 17-foot catamaran sailboat, have averaged 250 boats per month over the last 5 years with a standard deviation of 25 boats. Assuming that the demand is about the same as past years and follows a normal curve, what is the probability that sales will be less than 280 boats next month?

The lengths of human pregnancies are approximately normally distributed with a mean of 268 days and a standard deviation of 16 days. What is the probability that pregnancy lasts between 240 and 280 days?

Suppose that a brand of lightbulb lasts on average 1690 hours with a standard deviation of 194 hours. Assume the life of the lightbulb is normally distributed. Calculate the probability that a particular bulb will last from 1418 to 2183 hours?

Jeremiah earned a score of 530 on Exam A that had a mean of 450 and a standard deviation of 40. He is about to take Exam B that has a mean of 63 and a standard deviation of 20. How well must Jeremiah score on Exam B in order to do equivalently well as he did on Exam A? Assume that scores on each exam are normally distributed.

Customers arrive on average every 30 minutes to The Grease Monkey, an auto repair shop with only one mechanic. The inter-arrival times are exponentially distributed. Repair times are variable with a mean of 25 minutes and a standard deviation of 20 minutes. The mechanic works on one vehicle at a time from beginning to end and takes in any waiting vehicles on a first-come first-served basis. The garage itself has room for only one vehicle at a time, so waiting vehicles are kept in the parking lot where there are always plenty of spaces available. Assume customers never balk or renege. a)What is the average number of cars in the garage (not including the parking lot)? b) How long (in minutes) do vehicles wait on average in the adjacent parking lot? c) The competitor shop across the street also has a single mechanic and an average of 3.1 vehicles waiting in its parking lot. The competitor only does oil changes, which take an average of 21 minutes. Customer inter-arrival times to the…

A dean in the business school claims that GMAT scores of applicants to the school's MBA program have increased during the past 5 years. Five years ago, the mean and standard deviation of GMAT scores of MBA applicants were 550 and 60, respectively. 30 applications for this year's program were randomly selected and the GMAT scores recorded. If we assume that the distribution of GMAT scores of this year's applicants is the same as that of 5 years ago, find the probability of erroneously concluding that there is not enough evidence to supports the claim when, in fact, the true mean GMAT score is 590. Assume αα is 0.02.

In a recent year, grade 6 Ohio State public school students taking a mathematics assessment test had a mean score of 303.1 with a standard deviation of 36.  Possible test scores could range from 0 to 1000. Assume that the scores were normally distributed.  This is not a normal approximation, so do not correct for continuity. Find the probability that a student had a score higher than 295. Find the probability that a student had a score between 230 and 305. What is the highest score that would still place a student in the bottom 16% of the scores? If 4000 students are randomly selected, how many will have a test score that is less than 300? A random sample of 40 students is drawn from this population. What is the probability that the mean test score is greater than 290?

A manufacturer of light bulbs finds that one light bulb model has a mean life span of 1024 h with a standard deviation of 82 h.Find the z-scores for lightbulbs which last 810 and 890 h. (Round your answers to two decimal places.) 810 h: z = 890 h: z =

Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 36 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 4 months, and the distribution of lifetimes is normal.