A population of values has a normal distribution with \mu=204.3 and \sigma=43. You intend to draw a random sample of size n=111.Find the probability that

geduiwelh

geduiwelh

Answered question

2021-02-08

A population of values has a normal distribution with μ=204.3 and σ=43. You intend to draw a random sample of size n=111.
Find the probability that a single randomly selected value is less than 191.2.
P(X<191.2)=?
Find the probability that a sample of size n=111 is randomly selected with a mean less than 191.2.
P(M<191.2)=?
Write your answers as numbers accurate to 4 decimal places.

Answer & Explanation

l1koV

l1koV

Skilled2021-02-09Added 100 answers

Solution for Step 1: Make X a random variable.
Using the information provided, X exhibits a normal distribution with mean μ=204.3 and a standard deviation is σ=43.
Step 2 Next, determine the likelihood that a single randomly chosen figure will be less than 191.2.
P(X<191.2)=P(Xμσ<191.2204.343)
=P(Z<0.305)
=0.3802[Using the excel function=NORM.DIST(0.305,0,1,TRUE)]
As a result, 0.3802 percent chance exists that a single randomly chosen figure will be lower than 191.2.
Step 3
A sample size is determined from the provided data n=111.
Consequently, the likelihood that a randomly chosen sample has a mean below 191.2
P(M<191.2)=P(Mμσn<191.2204.343111)
=P(Z<111(13.1)43)
=P(Z<3.210)
=0.0007[Using the excel function =NORM.DIST(3.210,0,1,TRUE)]
Therefore, there is a 0.0007 percent chance that a randomly chosen sample has a mean below 191.2.

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