A fast food restaurant executive wishes to know how many fast food meals adults eat each week. They want to construct a 95% confidence interval with an error of no more than 0.07 meals. A consultant has informed them that a previous study found the mean to be 8.1 fast food meals per week and found the standard deviation to be 2.

What is the minimum sample size required to create the specified confidence interval?

Round your answer up to the next integer

Given Information:  

Confidence level = 95%  

Error = 0.07

Mean = μ = 8.1

Standard deviation = σ = 2

Required Information:  

Sample size = n = ?

Sample size = n ≤ 2209

Step-by-step explanation:  

The sample size required to create the specified confidence interval is given by

error ≤ z*(σ/√n)

Where z is the corresponding z-score of 95 percentile, n is the sample size and σ is the standard deviation and error is no more than 0.07

√n ≤ z*σ/error

n ≤ (z*σ/error)²

The z-score for 95% confidence level is 1.645

n ≤ (1.645*2/0.07)²

n ≤ 2209

Therefore, a sample size of n ≤ 2209 is required to create a 95% confidence interval with an error of no more than 0.07.

40 x 50 = 2000

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 ☺