Answer:
a) [tex]X\sim(27293,(7235)^2)[/tex]
b) 0.1567
c) [tex]P_{70}=31084.14[/tex]
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = $27,293 per year
Standard Deviation, σ = $7,235
We are given that the distribution of cost of college is a bell shaped distribution that is a normal distribution.
a) Distribution of X
Let X be the cost for a randomly selected college. Then,
[tex]X\sim (\mu, \sigma^2)\\X\sim(27293,(7235)^2)[/tex]
b) Probability that a randomly selected Private nonprofit four-year college will cost less than $20,000 per year.
[tex]P( x < 20000) = P( z < \displaystyle\frac{20000 - 27293}{7235}) = P(z < -1.008)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x < 20000) = 0.1567[/tex]
c) 70th percentile for the distribution.
We have to find the value of x such that the probability is 0.7
[tex]P( X < x) = P( z < \displaystyle\frac{x - 27293}{7235})=0.7[/tex]
Calculation the value from standard normal z table, we have,
[tex]\displaystyle\frac{x - 27293}{7235} = 0.524\\\\x = 31084.14[/tex]
The 70th percentile for the distribution of college cost is $31,084.14
