Question

On the basis of past experience, Martin Clothing Store manager estimates that the probability that any one customer will make a purchase is 0.30. Martin Clothing Store forecasts ten customers will enter the store in the next hour; the expected number of customers who will make a purchase is __________. The standard deviation for the number of customers who will make a purchase is __________. NOTE: Write your answers in number format, with 2 decimal places of precision level. Add a leading minus sign symbol, a leading zero and trailing zeros, when needed. Use a period for the decimal separator and a comma to separate groups of thousands.

Answer 1

This is the problem of binomial distribution.
X:any one customer will make a purchase or not.
P(X=1) = P(any one customer will make a purchase) = 0.30 = p
P(X=0) = P(any one customer will not make a purchase) = 1 - 0.30 = 0.70 = q
Question1: the expected number of customers who will make a purchase?
here n= 10,since they have given that 10 customers will enter the store.
For binary distribution:mean i.e. expected value of X = n*p
= 10*0.3
= 3
Question2: standard deviation for the number of customers who will make a purchase:
=sqrt(n*p*q)
=sqrt(10*0.3*0.7)
=1.449138

On the basis of past experience, Martin Clothing Store manager estimates that the probability that any one customer will make a purchase is 0.30. Martin Clothing Store forecasts ten customers will enter the store in the next hour; the expected number of customers who will make a purchase is 3. The standard deviation for the number of customers who will make a purchase is 1.45. NOTE: Write your answers in number format, with 2 decimal places of precision level. Add a leading minus sign symbol, a leading zero and trailing zeros, when needed. Use a period for the decimal separator and a comma to separate groups of thousands.