Mixed Practice – Central Limit Theorem
1)
Name _____________________________
Suppose 30% of all student at a university wear contact lenses.
a)
We randomly select 100 students. Let p̂ represent the proportion of students in this sample
who wear contacts. Can we use the normal distribution to approximate the distribution for p̂ ?
b)
Find the mean and standard deviation for p̂
c)
What is the probability that more than one-third of this sample wear contacts?
2)
It is believed that 4% of children have a gene that may be linked to juvenile diabetes. Researchers
hoping to track 20 of these children for several years test 732 newborns for the presence of this gene.
What is the probability that they find enough subjects for their study?
3)
Suppose the distribution for total amounts spent by students vacationing for a week in Florida is
normally distributed with a mean of $650 and a standard deviation of $120. What is the probability that
a group of 10 students will spend an average of between $600 and $700?
4)
State police believe that 70% of the drivers traveling on a major interstate highway exceed the speed
limit. They plan to set up a radar trap and check the speeds of 80 cars.
a)
Can we use the normal distribution to approximate the distribution for p̂ ?
b)
Find the mean and standard deviation for p̂
c)
What is the probability that less than 68% of the sample exceeds the speed limit?
5)
Suppose average outstanding credit balances for young couples is $650 with a standard deviation of
$420. If 100 couples are selected at random, what is the probability that the mean outstanding credit
card balance exceeds $700?
6)
Suppose the distribution of birth weights at a Boston hospital is approximately normal with mean 112
ounces and standard deviation 20.6 ounces. Find the probability that the average birth weight of the
next 20 babies born will be greater than 120 ounces.