Probability Ques.

Question

a normal distribution has a mean of 70 and a SD of 8. For each of the following scores, indicate whether the tail is to the right or left of the score and find the proportion in the tail (Hint: Find z scores).

a. 72

b. 76

c. 66

d. 60

Answer 1

Hello, thank you for taking the time to post your question!

For each part of these questions you want to start by finding the Z score using the formula

Z = (x – mean) / (standard deviation)

Once you have that value then you can convert it over into a proportion using either a normal distribution table or technology like Excel

So for example on the first part of the question here we would have

Z = (72 – 70) / 8 = 0.25

Then using a normal distribution table I find that that corresponds to a proportion value of 0.4013. Since the Z score here is positive that means that the proportion would be to the right.

Hopefully that helps get you moving in the right direction on these! You can use that same type of process on the remaining parts :)