The drying times for a certain type of cement are normally distributed with a standard deviation of 30 minutes. a researcher wishes to estimate the mean drying time for this type of cement. find the sample size needed to assure with 68.26% confidence that the sample mean will not differ from the population mean by more than 5 minutes.

a. 31
b. 26
c. 29
d. 38
e. 30
f. 27
g. 32
h. 36

h. 36

Step-by-step explanation:

For a 68.26% confidence, z = 1.0.

Standard deviation (s) = 30 minutes

The sample size needed to assure that the sample mean does not differ from the true mean by more than 5 minutes is given by:

The sample size needed is 36.

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 ☺

fd

step-by-step explanation: