A popular retail store knows that the purchase amounts by its customers is a random variable...

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.

Expert Solution

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)

orchestra answered 3 years ago

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