A population of values has a normal distribution with \mu = 133.5 and \sigma = 5.2. You intend to draw a random sample of size n = 230. Find the proba

Maiclubk 2021-03-18 Answered

A population of values has a normal distribution with μ=133.5 and σ=5.2. You intend to draw a random sample of size n=230.
Find the probability that a single randomly selected value is between 133.6 and 134.1.
P(133.6<X<134.1)=?
Write your answers as numbers accurate to 4 decimal places.

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Expert Answer

Clelioo
Answered 2021-03-19 Author has 88 answers

Given Information:
μ=133.5 and σ=5.2
n=230
To find the probability that a single randomly selected value is between 133.6 and 134.1:
z-score is a measure which tells how many standard deviations away a data value is from the mean and is given by the formula:
z=Xμσ
Required probability can be obtained as follows:
P(133.6<X<134.1)=P(X<134.1)P(X<133.6)
=P(Xμσ<134.1133.55.2)P(133.6133.55.2)
=P(Z<0.12)P(Z<0.02)
=0.547760.50798=0.03978 using standard table
Using a standard normal table, look up for z-score 0.12 i.e., 0.1 in the row and 0.02 along the column. The intersection of both values is 0.54776.
Similarly, probability corresponding to z-score 0.02 is 0.50798.
Then, subtract the lower probability value from the higher value.
Therefore, probability that a single randomly selected value is between 133.6 and 134.1 is 0.0398.

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Jeffrey Jordon
Answered 2021-11-14 Author has 2495 answers

Answer is given below (on video)

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