SOLUTION: 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 mea
Algebra.Com
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
RELATED QUESTIONS
Let X be the lifetime of an electronic device. It is known that the average lifetime of... (answered by Theo)
Let X be the lifetime of an electronic device. It is known that the average lifetime of... (answered by ewatrrr)
Hi,
I am really struglling with this question. It's a little tricky. Any help will be... (answered by stanbon)
1. The lifetime X of an electronic component has probability density function
f(x) =... (answered by stanbon)
PLEASE HELP ME!
THERE ARE 4 PART OF THE QUESTIONS TO THIS PROBLEM.
Revenues from an... (answered by Fombitz)
PLEASE HELP ME!
Revenues from an electronic device are shown in the table. Let P be... (answered by Fombitz,ewatrrr)
The time to repair an electronic device is a normally distributed random variable... (answered by richwmiller)
The time to repair an electronic device is a normally distributed random variable... (answered by stanbon)
The time to repair an electronic device is a normally distributed random variable... (answered by solver91311)