Scores of 50 college students who have taken a statistics test has a mean of 82 and a standard deviation of 5. Construct a 99 % confidence interval for the mean score. Also, report the critical value LaTeX: z_cz c corresponding to a confidence level of c

(80.1786, 83.8214)

Step-by-step explanation:

Confidence interval for population mean is given by :-

, where = Sample mean , n= sample size , = standard deviation, = critical z-value.

Given: n= 50,   ,

Critical z-value for 99% confidence level = 2.576

Now, a 99 % confidence interval for the mean:

Hence, required 99% confidence interval = (80.1786, 83.8214)

addition

step-by-step explanation:

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.