Normal Distribution probability question Please show all wor

Normal Distribution probability question.

Please show all working. Thanks!

If X is a normal random variable with mean 85 and standard deviation 10 compute the probability P(|X - 80| le 10) a, 0.5402 b. 0.7344 c. 0.6247 d. 0.4986 e. 0.4854

Solution

a) P(|x-80|<10} = P(70<x<90}

z score = (x-85)/10

Convert to z score. 70 becomes -15/10 =-1.5

90 becomes 5/10 =0.5

P(-1.5<z<0.5) = 0.3531+0.1915 = 0.5446

Hence option A.