For
instruction on how to use Minitab and Excel for the normal distribution, these
are found on page 248 (for probabilities) and page 255 (for percentiles) of the
textbook.
For the
following problems, all values were rounded to 4 decimals except as requested
in certain questions.
Sales at a
particular store are normally distributed with a mean of $30 and a standard
deviation of $12.50.
1)
What
is the probability that a sale is less than $35? (65.54%)
2)
What
is the probability that a sale is more than $50? (5.48%)
3)
What
is the probability that a sale is between $25 and $50? (60.06%)
4)
What
is the cutoff point for a sale to place in the top 10% of sales? Round to the
nearest dollar. ($46.00)
5)
If
a sample of 50 sales is taken, what is the probability the average of this
sample is less than $25? (0.23%)
6)
Suppose
a sample of 50 individual sales is taken and the mean of this sample is $29.50.
Construct a 95% confidence interval of the average sale at this store with the
margin of error rounded to 2 decimals. Interpret the interval. ($26.04 < m < $32.96)
7)
Suppose
they increase the level of confidence to 99% from 95%. How much does the margin
of error increase by? ($1.09)
8)
Suppose
they want to conduct another study. What should be the sample size if they use
the accepted standard deviation of $12.50 and they want the margin of error to
be no more than $2.50 and a level of confidence of 95%? (97)
9)
The
percentage of CO2 in Fizzy Soda follows a Beta distribution with a
mean of 75% and a standard deviation of 1.2%. Each hour, a sample of 60 cans is
taken and the average amount of CO2 is measured for quality control
purpose. They want the average percentage of CO2 to be between 74.7%
and 75.3%. In a sample of 60 cans, what is the probability of that happening?
(94.72%)
10)
A
survey of 200 people in the 18-34 age group showed that 84 of them own an Ipod. Construct a 95% confidence interval of the percentage
of Ipod users in this age group. Interpret the
interval. (0.3516 < p < 0.4884)
11)
Suppose
the researcher wanted to conduct a larger study. What would be the required
sample size if the researcher wanted a 3% margin of error at a 95% level of
confidence using the results of the study in question 10? (1040)
12)
Suppose
the researcher can afford no more than 500 surveys for a follow-up study. What
is the margin of error the researcher must live with? (4.33%)
13)
A
survey of 400 Canadian households is taken and the percentage in this sample
that watch Space on a weeknight is 0.75%. Construct a 95% confidence interval
of the percentage of Canadian households that watch Space.
(0.0016<p<0.0232)
14)
What
would the sample size need to be if the margin of error could be no more than
0.1% with a 95% level of confidence and the percentage of Canadians who watch
space is 0.75%? (46,953)
15)
Which
would have a greater effect on reducing the sample size in question 14:
decreasing the level of confidence to 90% or increasing the margin of error to
0.5%? (increase margin of error)
16)
Suppose
the CEO at Space won’t survey more than 1000 people. For a 95% level of
confidence, what would have been the margin of error used to calculate the
sample size of 1000? (0.69%)