SOLUTION: 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

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Question 1019501: 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
0.6789
0.7643
Answer by mathmate(429) About Me  (Show Source):
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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=%2865-70%29%2F4.5=-1.1111, P(Z<=-1.1111)=0.13326
X=80, Z=%2880-70%29%2F4.5=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.