Need help with statistic Question (Please show all steps)

Question

A variable is normally distributed with mean 68 and standard deviation 10. Find the percentage of all possible values of the variable that:
a. Lie between 73 and 80
b. Are at most 90

Answer 1

All you need to know to answer this question is that if you take your normal random variable (call it X) and we subtract the mean and divide by the standard deviation, you'll be left with a Normal(0,1) random variable).  Once you get a N(0,1), you can use a normal distribution table or software to calculate the probabilities.  

 

For example, let's say X~Normal with mean 50 and standard deviation 5.

P(40 < X < 60) = P(40-50 < X-50 < 60-50) <--subtract the mean

= P[(40-50)/5 < (X-50)/5 < (60-50)/5] <--divide by the standard deviation

= P[-2 < Z < 2] <---Z is Normal(0,1)

 

Now we can use a Normal table:

 

P[-2 < Z < 2] = P(Z < 2) - P(Z < -2)  <--since most tables use the left tail probabilities.

= .97725 - .02275 = .9545

 

Try using this technique on the problem you posted and let me know if you have any more questions!