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?

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 =

Standard deviation =

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

Formula :

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=-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=-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

really really sorry if i'm

-12 -5(x + 4) = 3x

-12 - 5x - 20 = 3x

-12 - 20 - 5x = 3x

-32 - 5x = 3x

    + 5x   + 5x

-32 = 8x

8         8

- 4= x