Non-standard Normal Problems.
Problem #1. Assume the mean STAND (like an SAT, but
healthier) score is 1028 with sd of 92. What is the 90th
percentile score? Oh you can't answer that. Assume STAND
scores follow a normal distribution.
What is the probability that a randomly selected score exceeds 1200?
Problem #2. If the average price of a new home is
$246,300 with a standard deviation of $15,000 find the minimum and
maximum prices of the houses that a contractor will build to satisfy
the middle 80% of the market. Assume that the variable is normally
distributed.
Problem #3. Americans drank an average of 34 gallons
of bottled water per capita in 2014. If the standard deviation
is 2.7 gallons and the variable is normally distributed, find the
probability that a randomly selected American drank more than 25
gallons of bottled water. What is the probability that the selected
person drank between 28 and 30 gallons?
Problem #4. What is the 70th percentile for an IQ
test? Assume that it is a normal distribution with mean 100
and standard deviation of 15.
CLT Problems
Problem #1. The average teacher’s salary in
Connecticut (ranked first among states) is $57,337. Suppose that the
distribution of salaries is normal with a standard deviation of
$7500.
a. What is the probability that a randomly selected teacher makes
less than $52,000 per year?
b. If we sample 100 teachers’ salaries, what is the probability that
the sample mean is less than $56,000?
Problem #2. The average age of chemical engineers is 37
years with a standard deviation of 4 years. If an engineering firm
employs 25 chemical engineers, find the probability that the average
age of the group is greater than 38.2 years old. If this is the
case, would it be safe to assume that the engineers in this group
are generally much older than average?