The probability that the total time taken by a random sample of 52 customers is less than 180 minutes is 0.02%.
μ=Population mean=4
σ=Population standard deviation=2
n=Sample size=50
The sampling distribution of the sum S is roughly normal if the sample size is big (30 or more), according to the central limit theorem.
The central limit theorem tells us that the sampling distribution of the sum S is about normal because the sample size of 50 is at least 30.
The sum S's sample distribution has a mean and standard deviation of n and n, respectively.
The z-score is the value decreased by the mean, divided by the standard deviation
z = ( x -μS ) / √σS
= 150 - 50(4) / √ 50(2)
= 3.54
Using the appendix's normal probability table, get the relevant probability,
P(S < 150 ) = P(Z< -3.54)
= 0.0002
=0.02%
The term "standard deviation" refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
To learn more about standard deviation
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