A population of values has a normal distribution with \mu = 49 and \sigma = 79.5. You intend to draw a random sample of size n=84. Find the probabilit

glasskerfu 2020-10-27 Answered
A population of values has a normal distribution with μ=49 and σ=79.5. You intend to draw a random sample of size n=84.
Find the probability that a a sample of size n=84 is randomly selected with a mean greater than 72.4.
P(M>72.4)=?
Write your answers as numbers accurate to 4 decimal places.
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Expert Answer

tafzijdeq
Answered 2020-10-28 Author has 92 answers
Step 1
Given,
Mean = 49
Standard deviation = 79.5
Sample size = 84
Step 2
Consider,
P(M>72.4)=P(Mμσn>72.4μσn)
=P(Z>72.4μσn)
=P(Z>72.44979.584)
=P(Z>2.70)
=1P(Z2.70)
=10.9965=0.0035 (Using standard normal table)
The probability that a sample of size n=84 is randomly selected with a mean greater than 72.4 is, 0.0035.
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