A department store wants to know what fraction of its customers in a certain market have store credit cards, and what their average balance might be. Of the 120 customers surveyed, 30 had store credit cards. Amongst those customers, the average balance was $600, with a sample standard deviation of $80. Find the 98% confidence interval for the average credit card balance. ( , ) Round your answers to two decimal places.

The 98% confidence interval for the average credit card balance is

(564.04, 635.96).

Step-by-step explanation:

We have to calculate the 98% confidence interval on the average credit card balance.

The sample will consist of the n=30 customers that have credit card.

The sample has a mean of $600 and a standard deviation of $80.

As the population standard deviation is estimated from the sample standard deviation, we will use a t statistic.

The degrees of freedom are:

The critical value for a 98% CI and 29 degrees of freedom is t=2.463 (this can be looked up in a t-table).

Then, the margin of error is:

Then, the upper and lower bounds of the confidence interval are:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

yes   because as the functions are graphed they eventually will intersect unless otherwise

step-by-step explanation: