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

waigaK 2020-11-22 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 single randomly selected value is between 198.5 and 205.6.
P(198.5<X<205.6)=?
Write your answers as numbers accurate to 4 decimal places.

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Expert Answer

Adnaan Franks
Answered 2020-11-23 Author has 92 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
The required probability that a single randomly selected value is between 198.5 and 205.6 can be obtained as:
P(198.5<X<205.6)=P(198.519768<xμσ<205.619768)
=P(0.022<Z<0.126)
=P(Z<0.126)P(Z<0.022)
=0.55010.5088=0.0413 (Using standard normal table)
Thus, the required probability is 0.0413.

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