Question

The prices of condos in a city are normally distributed with a mean of $100,000 and a standard deviation of $32,000.

Answer the following questions rounding your solutions to 4 decimal places.

1. The city government exempts the cheapest 6% of the condos from city taxes. What is the maximum price of the condos that will be exempt from city taxes?

2. If 2% of the most expensive condos are subject to a luxury tax, what is the minimum price of condos that will be subject to the luxury tax?

A professor at a local university noted that the grades of her students were normally distributed with a mean of 73 and a standard deviation of 11.

Answer the following questions rounding your solutions to 4 decimal places.

1. The professor has informed the class that 7.93 percent of her students received grades of A. What is the minimum score needed to receive a grade of A?

2. Students who made 57.93 or lower on the exam failed the course. What fraction of students failed the course?

3. If 69.5 percent of the students received grades of C or better, what is the minimum score of those who received C's?

Answer 1

This is a normal distribution question with

1) Given in the question
P(X < x) = 0.06
This implies that
P(Z < -1.555) = 0.06
With the help of formula for z, we can say that

x = 50247.245
2) Given in the question
P(X < x) = 0.98
This implies that
P(Z < 2.0538) = 0.98
With the help of formula for z, we can say that

x = 165719.9651

This is a normal distribution question with

1) Given in the question
P(X < x) = 0.9207
This implies that
P(Z < 1.41) = 0.9207
With the help of formula for z, we can say that

2) x = 57.93
P(x < 57.93)=?
The z-score at x = 57.93 is,

z = -1.37
This implies that
P(x < 57.93) = P(z < -1.37) = 0.085
3) Given in the question
P(X < x) = 0.305
This implies that
P(Z < -0.51) = 0.305
With the help of formula for z, we can say that

x = 67.3892
PS: you have to refer z score table to find the final probabilities.
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