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 2 years agoRelated Solutions
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