An anthropologist wishes to estimate the average height of men for a certain rac
ID: 3128281 • Letter: A
Question
An anthropologist wishes to estimate the average height of men for a certain race of people. If the population standard deviation is assumed to be 2.5 inches and if she randomly samples 100 men, find the probability that the difference between the sample mean and the true population mean will not exceed.5 inch. Twenty-five heat lamps are connected in a greenhouse so that when one lamp fails, another takes over immediately. (Only one lamp is turned on at any time.) The lamps operate independently, and each has a mean life of 50 hours and standard deviation of 4 hours. If the greenhouse is not checked for 1300 hours after the lamp system is turned on, what is the probability that a lamp will be burning at the end of the 13(X)-hour period?Explanation / Answer
PROBLEM 4.
Note that the mean difference of sample emans from the population mean is 0.
We first get the z score for the two values. As z = (x - u) sqrt(n) / s, then as
x1 = lower bound = -0.5
x2 = upper bound = 0.5
u = mean = 0
n = sample size = 100
s = standard deviation = 2.5
Thus, the two z scores are
z1 = lower z score = (x1 - u) * sqrt(n) / s = -2
z2 = upper z score = (x2 - u) * sqrt(n) / s = 2
Using table/technology, the left tailed areas between these z scores is
P(z < z1) = 0.022750132
P(z < z2) = 0.977249868
Thus, the area between them, by subtracting these areas, is
P(z1 < z < z2) = 0.954499736 [ANSWER]
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