An education finance corporation claims that the average cre

An education finance corporation claims that the average credit card debts carried by undergraduates are normally distributed, with a mean of $3173 and a standard deviation of $1120.

What is the probability that a randomly selected undergraduate, who is a credit card holder, has a credit card balance less than $2700?

You randomly select 25 undergraduates who are credit card holders. What is the probability that their mean credit card balance is less than $2700?

Step by step answer if possible

Solution

An education finance corporation claims that the average credit card debts carried by undergraduates are normally distributed, with a mean of $3173 and a standard deviation of $1120.

What is the probability that a randomly selected undergraduate, who is a credit card holder, has a credit card balance less than $2700?

Z value for 2700,   z= (2700-3173)/1120 = -0.4223   = -0.42( 2 decimals)

P( x <2700) = p( z < -0.42) = 0.3372

You randomly select 25 undergraduates who are credit card holders. What is the probability that their mean credit card balance is less than $2700?

Step by step answer if possible

Standard error = 1120 /sqrt(25) =224

Z value for 2700,   z= (2700-3173)/224 = -2.1116   = -2.11( 2 decimals)

P( mean x <2700) = p( z < -2.11) = 0.0174