A population of values has a normal distribution with \mu = 116.5 and \sigma = 63.7. You intend to draw a random sample of size n = 244.

Wribreeminsl 2020-11-29 Answered

A population of values has a normal distribution with μ=116.5 and σ=63.7. You intend to draw a random sample of size n=244.
Find the probability that a sample of size n=244 is randomly selected with a mean between 104.7 and 112.8.
P(104.7<M<112.8)=?
Write your answers as numbers accurate to 4 decimal places.

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Expert Answer

Aubree Mcintyre
Answered 2020-11-30 Author has 73 answers

A population of values has a normal distribution with μ=116.5 and σ=63.7.
A random sample of size (n)=244 is drawn.
We need to find the probability that a sample of size n=244 is randomly selected with a mean(M) between 104.7 and 112.8.
MN(116.5,63.72n) and n=244
So, Z=n(M116.5)63.7N(0,1)
Thus, P[104.7<M<112.8]
=P[n(104.7116.5)63.7<n(M116.5)63.7<n(112.8116.5)63.7]
=P[2.893<Z<0.9073]
=P[Z0.9073]P[Z2.8934]
=0.18210.0019=0.1802
So, the probability that a sample of size n=244 is randomly selected with a mean between 104.7 and 112.8 is 0.1802.

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