A population of values has a normal distribution with \mu=197 and \sigma=68.

ka1leE 2021-01-28 Answered

A population of values has a normal distribution with μ=197 and σ=68. You intend to draw a random sample of size n=181
Find the probability that a sample of size n=181 is randomly selected with a mean between 198.5 and 205.6.
P(198.5<M<205.6)=?
Write your answers as numbers accurate to 4 decimal places.

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Expert Answer

faldduE
Answered 2021-01-29 Author has 109 answers

Step 1
From the provided information,
Mean (μ)=197
Standard deviation (σ)=68
Let X be a random variable which represents the value.
XN(197,68)
Step 2
Sample size (n)=181
The required probability that a sample of size n=181 is randomly selected with a mean between 198.5 and 205.6 P(198.5<M<205.6) can be obtained as:
P(198.5<M<205.6)=P(198.519768181<Mμσ181<205.619768181)
=P(0.297<Z<1.701)
=P(Z<1.701)P(Z<0.297)
=0.95550.6168=0.3387 (Using standard normal table)
Thus, the required probability is 0.3387.

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