A population of values has a normal distribution with \mu=221.6 and \sigma=44.1. You intend to draw a random sample of size n=42. Find the probability

mattgondek4 2021-02-21 Answered

A population of values has a normal distribution with μ=221.6 and σ=44.1. You intend to draw a random sample of size n=42.
Find the probability that a single randomly selected value is between 221.6 and 229.1.
P(221.6<X<229.1)=?
Write your answers as numbers accurate to 4 decimal places.

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Expert Answer

Maciej Morrow
Answered 2021-02-22 Author has 98 answers

Step 1
Given information-
Population mean,μ=221.6
Population standard deviation, σ=44.1
Sample size, n=42
Let, X be the randomly selected value is approximately normally distributed.
XN(221.6,44.1)
Step 2
The probability that a single randomly selected value is between 221.6 and 229.1 is P(221.6<X<229.1)=
P(221.6<X<229.1)=P(221.6221.644.11<Xμσn<229.1221.644.11)
P(221.6<X<229.1)=P(0<Z<0.1701)
P(221.6<X<229.1)=P(Z<0.170)P(Z<0)
P(221.6<X<229.1)=0.56750.5=0.0675
(From excel using formula = NORM.S. DIST (0.170,TRUE))
(From excel using formula = NORM.S. DIST (0,TRUE))
Hence, the probability that a single randomly selected value is between 221.6 and 229.1 is 0.0675.

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