Question

hey I have trouble solving this

In 2016 it was determined that the credit card debt among adults in the US under the age of 35 was normally distributed with a mean of $5,808 and a standard deviation of $1,950.

Draw a complete graph of each situation and find the answer. One point will be given for a correct graph and one point for the final answer on a, b and c. Four points are possible for part d: one for the graph and one point each for the quartiles.

a. What percent of these adults have credit card debt that is more than $7,000?

b. What percent of these adults have credit card debt that is less than $3,000?

c. What percent of these adults have credit card debt that is between $4, 000 and $6,500?

d. What are the three quartiles for the distribution described above?

Answer 1

a)

P(X > 7000) = P(z > (7000 - 5808)/1950) = P(z > 0.6113) = 0.2705

b)

P(X < 3000) = P(z < (3000 - 5808)/1950) = P(z < -1.44) = 0.0749

c)

P(4000 < X < 6500) = P((4000 - 5808)/1950 < z < (6500 - 5808)/1950) = P(-0.9272 < z < 0.3549) = 0.4617

D)

Q1 = 4493.331

Q2 - 5808

Q3 - 7122.669