Installation of certain hardware takes a random amount of time. The installation times form a normally distributed distribution with a standard deviation 5 minutes and a mean of 45 minutes. A computer technician installs the hardware on 31 different computers. You are interested to find the probability that the mean installation time for the 31 computers is less than 43 minutes.

Select the most appropriate item that pertains to the problem.

a. z=-0.4
b. none of these
c. z=-2.23
d. z=2.23

And,
What is the probability that the mean installation time for 31 computers is less than 43 minutes?

a. 0.400
b. 0.345
c. none of these
d. 0.0129
e. 0.987

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fichoh fichoh · Answer 1 · 2021-08-06T16:33:19+02:00

The most appropriate values are:

z = - 2.23

The corresponding probability is : 0.01297

Mean, μ = 45

Standard deviation, σ = 5

Sample size, n = 31

The standard score, Z ; Since distribution is normal is obtained thus;

Z= (x - μ) ÷ (σ/√n)

For, x = 43

Z = (43 - 45) ÷ (5/√31)

Z = - 2.227

The probability :

Using the standard normal distribution table:

P(Z < - 2.227)

P = 0.01297

Hence, Z = - 2.23

P(x ≤ 43) = 0.0129

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