A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 48.0 and 53.0 minutes. Find the probability that a given class period runs between 50.5 and 50.75 minutes.

Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is less than 2.17 and draw a sketch of the region.

Assume that adults have IQ scores that are normally distributed with a mean of 109 and a standard deviation of 15. Find the third quartile Q3, that is the IQ score separating the top 25% from the others.Find the indicated IQ score. The graph below depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.(area to left of x is 65%)Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.Assume that adults have IQ scores that are normally distributed with a mean of mu =100 and a standard deviation sigma = 20. Find the probability that a randomly selected adult has an IQ less than 128.Assume that adults have IQ scores that are normally distributed with a mean of 100and a standard deviation 20. Find P14, which is the IQ score separating the bottom 14% from the top 86%.A survey found that women's heights are normally distributed with mean 63.7 in and standard deviation 2.2 in. A branch of the military requires women's heights to be between 58 in and 80 in.a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or too tall?b. If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new heightrequirements?Why might they do this?