Question

Private nonprofit four-year colleges charge, on average, $27,293 per year in tuition and fees. The standard deviation is $7,235. Assume the distribution is normal. Let X be the cost for a randomly selected college. Round all answers to two decimal places.
A. X ~ N( ____ , _____ )

B. Find the probability that a randomly selected Private nonprofit four-year college will cost less than $20,000 per year.

C.Find the 70th percentile for this distribution.

Answer 1

Answer:

a) $X\sim(27293,(7235)^2)$

b) 0.1567

c) $P_{70}=31084.14$

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,

$X\sim (\mu, \sigma^2)\\X\sim(27293,(7235)^2)$

b) Probability that a randomly selected Private nonprofit four-year college will cost less than $20,000 per year.

$P( x < 20000) = P( z < \displaystyle\frac{20000 - 27293}{7235}) = P(z < -1.008)$

Calculation the value from standard normal z table, we have,  

$P(x < 20000) = 0.1567$

c) 70th percentile for the distribution.

We have to find the value of x such that the probability is 0.7

$P( X < x) = P( z < \displaystyle\frac{x - 27293}{7235})=0.7$  

Calculation the value from standard normal z table, we have,  

$\displaystyle\frac{x - 27293}{7235} = 0.524\\\\x = 31084.14$  

The 70th percentile for the distribution of college cost is $31,084.14