Question 1019501
 
Question:
Suppose you have a normal distribution of values with a mean of 70 and a standard deviation of 4.5 find the probability that a given value in the distribution is between 65 and 80 inclusively. Use the Z formula to solve the question. 
A. 0.85361
B. 0.956
C. 0.6789
D. 0.7643
 
Solution:
μ=70; σ=4.5;
convert X to Z :  Z=(X-μ)/σ
X=65, Z={{{(65-70)/4.5}}}=-1.1111, P(Z<=-1.1111)=0.13326
X=80, Z={{{(80-70)/4.5}}}=2.2222, P(Z<=2.2222)=0.98687
Therefore 
P(65<=X<=80)=0.98687-0.13326=0.85361
 
Answer: Probability that the value is between 65 and 80 is 0.85361 approximately.