The Survey of Earned Doctorates published by Statistics Canada revealed that doctoral candidates required, on average, 68 months to earn their Ph.D. degrees. If time to completion is normally distributed with a standard deviation of 13 months, find the probability that a doctoral candidate will earn a Ph.D. degree in: (Round to 4 decimals) a. Less than 5 years. b. Between 5 and 6 years. c. More than 5.5 years. d. More than 6 years. e. Between 4.5 and 5.5 years.

On a particular college campus, 21% of the students belong to a fraternity or sorority. If 49 college students are randomly chosen: a. What is the probability that no more than 12 are members of a fraternity or sorority? Round to at least three decimal places. b. What is the mean of this distribution? Round to at least one decimal. c. What is the standard deviation of this distribution? Round to at least one decimal.

the heights of 18-year old men are approximately normally distributed with a mean of U= 68 inches and a standard deviation of O=3. what is the probability that an 18-year-old mean selected at random is less than 65 inches tall.   a .8413 b .1587 c .1389 d .8765

Furnace repair bills are normally distributed with a mean of 271 dollars and a standard deviation of 20 dollars. If 64 of these repair bills are randomly selected, find the probability that they have a mean cost between 271 dollars and 273 dollars. Round to four decimal places. A. 0.2881 OB. 0.2119 O C. 0.5517 O D. 0.7881