In: Statistics and Probability
A popular retail store knows that the purchase amounts by its customers is a random variable that follows a normal distribution with a mean of $30 and a standard deviation of $9. What is the probability that a randomly selected customer will spend between $20 and $35 at this store? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.3456 would be a legitimate entry.
µ = 30
σ = 9
we need to calculate probability for ,
20 ≤ X ≤ 35
X1 = 20 , X2 =
35
Z1 = (X1 - µ ) / σ = -1.111
Z2 = (X2 - µ ) / σ = 0.556
P ( 20 < X <
35 ) = P (
-1.111111111 < Z < 0.556
)
= P ( Z < 0.556 ) - P ( Z
< -1.111 ) =
0.7107 - 0.1333 =
0.5775(answer)
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excel for probability from z score
=normsdist(z)