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A normal distribution has a mean of μ=54 and a standard deviation of σ=6. What is the probability of randomly selecting a score less than X=51? What is the probability of selecting a Random sample of n=4scores with a mean less than m=51? What is the probability of selecting a sample of n=36scores with a mean less than m=51?

Answer :

Answer:

A)The probability of randomly selecting a score less than X=51 is 0.3085

B)The probability of selecting a Random sample of n=4scores with a mean less than m=51 is 0.1587

C)The probability of selecting a sample of n=36scores with a mean less than m=51 is 0.0013

Step-by-step explanation:

Mean =[tex]\mu = 54[/tex]

Standard deviation =[tex]\sigma = 6[/tex]

A)What is the probability of randomly selecting a score less than X=51 i.e. P(x<51)?

Formula : [tex]Z =\frac{x-\mu}{\sigma}[/tex]

[tex]Z=\frac{51-54}{6}[/tex]

Z=-0.5

Refer the Z table for p value

So, P(x<51)=0.3085

So,the probability of randomly selecting a score less than X=51 is 0.3085

B)What is the probability of selecting a Random sample of n=4scores with a mean less than m=51?

Formula : [tex]Z =\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z=\frac{51-54}{\frac{6}{\sqrt{4}}}[/tex]

Z=-1

Refer the Z table for p value

So, P(x<51)=0.1587

So, the probability of selecting a Random sample of n=4scores with a mean less than m=51 is 0.1587

C) What is the probability of selecting a sample of n=36scores with a mean less than m=51?

Formula : [tex]Z =\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z=\frac{51-54}{\frac{6}{\sqrt{36}}}[/tex]

Z=-3

Refer the Z table for p value

So, P(x<51)=0.0013

So,the probability of selecting a sample of n=36scores with a mean less than m=51 is 0.0013

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