Question

The mean volume of customer traffic in a new store is 927 people per week with a standard deviation of 86. Answer the following questions based on these data. Write out what P() would be for each.

a. What is the probability that more than 1,000 customers visit the store in a given week?

b. What is the probability that less than 800 customers visit the store in a given week?

c. What is the probability that between 900 and 1050 customers visit the store in a given week?

Answer 1

Solution :

Given that,

mean = = 927

standard deviation = = 86

a ) P (x > 1,000 )

= 1 - P (x < 1,000 )

= 1 - P ( x -  / ) < ( 1,000 - 927 / 86)

= 1 - P ( z <  73 / 86 )

= 1 - P ( z < 0.85 )

Using z table

= 1 - 0.8023

= 0.1977

Probability = 0.1977

b ) P( x < 800 )

P ( x - / ) < ( 800 - 927 / 86)

P ( z < -127 / 86 )

P ( z < -1.48)

= 0.0694

Probability = 0.0694

c ) P (900 < x < 1050 )

P ( 900 - 927 / 86) < ( x -  / ) < ( 1050 - 927 / 86)

P ( - 27 / 86 < z < 123 / 86)

P (-0.31 < z < 1.43 )

P ( z < 1.43 ) - P ( z < -0.31)

Using z table

= 0.9236 - 0.3782

= 0.5454

Probability = 0.5454