A population of values has a normal distribution with

a2linetagadaW 2021-01-19 Answered

A population of values has a normal distribution with μ=200.7 and σ=10. You intend to draw a random sample of size n=178
Find the probability that a sample of size n=178 is randomly selected with a mean less than 198.6.
P(M<198.6)=?

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Expert Answer

tabuordg
Answered 2021-01-20 Author has 99 answers

Step 1
From the provided information,
Mean (μ)=200.7
Standard deviation (σ)=10
Let X be a random variable which represents the value.
XN(200.7,10)
Sample size (n)=178
Step 2
The required probability that a sample of size n=178 is randomly selected with a mean less than 198.6 can be obtained as:
P(M<198.6)=P(Mμσn<198.6200.710178)
=P(Z<2.802)=0.0025 (Using standard normal table)
Thus, the required probability is 0.0025.

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