Question 1079953: The distribution of heights of adult men in the U.S. is approximately normal with mean 69 inches and standard deviation 2.5 inches. Use what you know about a normal distribution and the 68-95-99.7 rule to answer the following.
NOTE: If your answer is a percent, such as 25 percent, enter: "25 PERCENT" (without the quotes). If your answer is in inches, such as 10 inches, enter: "10 INCHES" (without the quotes and with a space between the number and the INCHES). If your answer is an interval, such as 14 to 15 inches, then enter: "14 TO 15 INCHES" (without the quotes). Do not use extra zeros and do not include a decimal point unless your answer is not a whole number. Your answer must be entered in the correct format.
(a) About what percent of men are between 69 and 74 inches?
(b) Fill in the blank: About 2.5 percent of all men are shorter than ________.
(c) Between what approximate heights do the middle 95 percent of men fall?
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! 68–95–99.7 rule tells us the percentage of values that lie around the mean in a normal distribution with a width of one, two and three standard deviations
:
a) 74 is two standard deviations from the mean, therefore 34 percent + 13.5 percent = 47.5 percent. Note that we had to take half of 68 percent and half of (95 percent - 68 percent).
:
b) 2.5 percent is approximately 2 standard deviations from the mean, therefore 2 * 2.5 = 5 and 69 - 5 = 64 inches
:
c) the middle 95 percent of men fall between 2 standard deviations of the mean, therefore the middle 95 percent is 64 to 74 inches
:
|
|
|
