the commute times for workers in a city are normally distributed with an unknown population mean and standard deviation. if a random sample of 37 workers is taken and results in a sample mean of 31 minutes and sample standard deviation of 5 minutes, find a 95% confidence interval estimate for the population mean using the student's t-distribution.

The 95% confidence interval for the population mean commute time is between 29.33 minutes and 32.67 minutes.

Step-by-step explanation:

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 37 - 1 = 36

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 36 degrees of freedom(y-axis) and a confidence level of . So we have T = 2.0262

The margin of error is:

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 31 - 1.67 = 29.33 minutes

The upper end of the interval is the sample mean added to M. So it is 31 + 1.67 = 32.67 minutes.

The 95% confidence interval for the population mean commute time is between 29.33 minutes and 32.67 minutes.

answer: '

the distance between points l and m

step-by-step explanation:

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺