A car-rental company is interested in the amount of time its vehicles are out of operation for repair work. state all assumptions and find a 90% confidence interval for the mean number of days in a year that all vehicles in the company's fleet are out of operation if a random sample of 10 cars showed the following number of days that each had been inoperative. 10 13 20 15 17 22 8 14 19 7 state all assumptions. select all the assumptions below. a. the sample comes from a normal population b. the sample size is at least 30 c. it is a random sample d. the variance is less than the mean find a 90% confidence interval for the population mean. the 90% confidence interval is from a lower limit of nothing to an upper limit of nothing. (round to two decimal places as needed.)

13.57 < µ < 15.43

Step-by-step explanation:

Assume:  We have to assume the sample comes from a normally distributed population because we do not know the population standard deviation.  

We assume that it was a random sample.

Do not assume:  The sample size is at least 30 because we are that it's 10.  Don't assume the variance is less than the mean because we can calculate it and will know for sure.

To find a 90% confidence interval we need to find the sample mean and sample standard deviation.  See attached photo 1 for the calculations

See attached photo 2 for the construction of the confidence interval

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47