Question

In: Statistics and Probability

Suppose x represents the dollar amount spent on supermarket impulse buying (in the checkout line). Based...

Suppose x represents the dollar amount spent on supermarket impulse buying (in the checkout line). Based on a certain article, the population mean is µ = $32 and the standard deviation is about σ = $8.

a) Considering that we have a random sample of n = 90 customers, who have done some impulse buying at the supermarket. From the Central Limit Theorem, what can you say about the ¯x distribution.

b) What is µx¯?

c) Find the standard deviation of the sample mean, σx¯.

d) What is the probability that ¯x is less than $30?

e) What is the probability that ¯x is more than $33?

Solutions

Expert Solution

Solution :

Given that ,

mean = = 32

standard deviation = = 8

n = 90

a) The sampling distribution of is approximately normal,

b) = = 32

c) = / n = 8 / 90 = 0.843

d) P( < 30) = P(( - ) / < (30 - 32) / 0.843 )

= P(z < -2.37)

Using z table

= 0.0089

e) P( > 33) = 1 - P( < 33)

= 1 - P[( - ) / < (33 - 32) / 0.843 ]

= 1 - P(z < 1.19)

Using z table,

= 1 - 0.8830

= 0.1170

orchestra answered 1 year ago

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