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?