Question

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 1

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 =$\mu = 54$

Standard deviation =$\sigma = 6$

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

Formula : $Z =\frac{x-\mu}{\sigma}$

$Z=\frac{51-54}{6}$

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 : $Z =\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

$Z=\frac{51-54}{\frac{6}{\sqrt{4}}}$

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 : $Z =\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

$Z=\frac{51-54}{\frac{6}{\sqrt{36}}}$

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