Question

According to a poll on consumer​ behavior, 36​% of people say they will only consider cars manufactured in their country when purchasing a new car. Suppose you select a random sample of 100 respondents. Complete parts​ (a) through​ (c) below.

a. What is the probability that the sample will have between 35​% and 45​% who say they will consider only cars manufactured by a company in their country when purchasing a new​ car? The probability is 0.5521. ​(Round to four decimal places as​ needed.)

b. The probability is 80​% that the sample will be contained within what symmetrical limits of the population​ percentage? The probability is 80​% that the sample percentage will be contained above 29.8​% and below 42.2​%. ​(Round to one decimal place as​ needed.)

c. The probability is 68​% that the sample will be contained within what symmetrical limits of the population​ percentage? The probability is 68​% that the sample percentage will be contained above 31.2​% and below 40.8​%. ​(Round to one decimal place as​ needed.)

How to solve in excel I already have answers but dont know how to do on excel.

Answer 1

In excel we have to use z test function (formula bar-> statistical functions->z test) ,

(formula bar-> statistical functions-> STDEV)

mean=36

upper limit=45

lower limit= 35

N=100

use z test function in excel

array = numbers from 1 to 100

x= 35 and 45

sigma =standard deviation . you can calculate it in excel using standard deviation function using array 1 to 100

z score comes out to be 0.028 for upper limit 45 (rounded off to 0.03)

then use the z table to calculate P value against z score i.e. 0.5120

similarly calculate for lower limit.

b) now we have P value. we will look for z score against it and using it we can calculate upper and lower limit.

use formula in excel, Z score for 80% probability =36-lower limit/ sigma

or, lower limit= 36- (z*sigma)

for upper limit, Z=upper limit - 36/sigma

or, upper limit= (Z*sigma) +36

c) you can solve it using z score against probality 68% using similar method as above. symmetrical limits means you can consider it to be a normal curve and use z score.