Exam 7: Continuous Probability Distributions

TotCo is developing a new deluxe baby bassinet.If the length of a newborn baby is normally distributed with a mean of 50 cm and a standard deviation of 5 cm,what should be the interior length of the bassinet to ensure that 99 percent of newborn babies will fit,with a safety margin of 15 cm on each end of the bassinet?

If the mean waiting time for the next arrival is 18 minutes,what is the first quartile (25th percentile)for waiting times?

The lengths of brook trout caught in a certain Colorado stream are normally distributed with a mean of 14 inches and a standard deviation of 3 inches.What proportion of brook trout caught will be between 12 and 18 inches in length?

If the random variable Z has a standard normal distribution,then P(Z ≤ − 1.37)is

To convert a normally distributed variable X into a standard Z score we would

A machine dispenses water into a glass.Assuming that the amount of water dispensed follows a continuous uniform distribution from 10 ounces to 16 ounces,what is the probability that 13 or more ounces will be dispensed in a given glass?

A certain assembly line at Vexing Manufacturing Company averages 30 minutes between breakdowns.What is the probability that less than 6 minutes will elapse before the next breakdown?

Bob's z-score for the last exam was 1.52 in Prof.Axolotl's class BIO 417,"Life Cycle of the Ornithorhynchus." Bob said,"Oh,good,my score is in the top 10 percent." Assuming a normal distribution of scores,is Bob right?

On the last exam in FIN 417,"Capital Budgeting Strategies" Bob's z-score was −1.15.Bob said,"Yipe! My score is within the bottom quartile." Assuming a normal distribution,is Bob right?

The normal distribution is a good approximation to the binomial if n = 25 and π = .50.

If arrivals follow a Poisson distribution,waiting times follow the exponential distribution.

The lengths of brook trout caught in a certain Colorado stream are normally distributed with a mean of 14 inches and a standard deviation of 3 inches.What lower limit should the State Game Commission set on length if it is desired that 80 percent of the catch may be kept by fishers?

A large number of applicants for admission to graduate study in business are given an aptitude test.Scores are normally distributed with a mean of 460 and standard deviation of 80.What fraction of the applicants would you expect to have a score of 400 or above?

A large number of applicants for admission to graduate study in business are given an aptitude test.Scores are normally distributed with a mean of 460 and standard deviation of 80.What fraction of applicants would you expect to have scores of 600 or above?

For a continuous uniform distribution U(200,400),the parameters are μ = 300 and σ = 100.

The height and width of a continuous uniform distribution's PDF are the same.

If the random variable Z has a standard normal distribution,then P(1.25 ≤ Z ≤ 2.17)is

In a True-False exam with 100 questions,passing requires a score of at least 60.What is the approximate normal probability that a "guesser" will score at least 60 points?

If arrivals occur at a mean rate of 2.6 events per minute,the exponential probability of waiting more than 1.5 minutes for the next arrival is

The exponential distribution can be either right-skewed or left-skewed,depending on λ.