Question 915836: Let X be the lifetime of an electronic device. It is known that the average lifetime of the device is 767 days and the standard deviation is 142 days. Let xˉ be the sample mean of the lifetimes of 210 devices. The distribution of X is unknown, however, the distribution of xˉ should be approximately normal according to the Central Limit Theorem. Calculate the following probabilities using the normal approximation.
(a) P(xˉ≤752)
(b) P(xˉ≥784)
(c) P(749≤xˉ≤781)
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website! mean = 767 days and sd = 142 days
 , z(752)= -15/142, z(784) = 17/142
a. P( z ≤ -15/142) = normalcdf(-100, -.1056) = .4579 0r 45.79%
b. P( z ≥ 17/142) = normalcdf(.1197, 100) = .4524 0r 45.24%
c. P( -18/142 < z < 14/142) = normalcdf(-.1268, .0986)= .5393 - .4495
0r P(749 < x < 781) = normalcdf(749,781,767,142)
Note: practice checking the arithmetic
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