Question

The Nike annual report states that Nike is one of the largest sellers of athletic footwear in the world. Nike's footwear products are primarily designed for athletic use, but also for casual and leisure wear. Historical data indicates that the average customer buys 4.7 pairs of sports shoes per year, with a population standard deviation of 4.6. If samples of 45 customers are taken, answer the following questions.
Your answers should be accurate to 2 decimal places.
a) What is the standard error of the mean for the sample means?

b) What is the probability that the a given sample mean is between 3 and 5 pairs of shoes?

c) What is the probability that the difference between a given sample mean and the population mean is less than 0.19?

d) What is the probability a given sample mean is greater than 5 pairs?

Answer 1

a)

standard error of the mean for the sample means = = 4.6/

= 0.6857275

b)

probability that the a given sample mean is between 3 and 5 pairs of shoes

= P(3 < < 5)

= P( < 5) - P( < 3)

= P[Z < (5 - 4.7)/0.6857275] - P[Z < (3 - 4.7)/0.6857275]

= P[Z < 0.44] - P[Z < -2.48]

= 0.6700 - 0.0066

= 0.6634

c)

probability that the difference between a given sample mean and the population mean is less than 0.19

= P( - 4.7 < 0.19)

= P( < 4.89)

= P[Z < (4.89 - 4.7)/0.6857275]

= P[Z < 0.28]

= 0.6103

d)

probability a given sample mean is greater than 5 pairs

= P( > 5)

= P[Z < (5 - 4.7)/0.6857275]

= P[Z > 0.44]

= 0.3300