Question

Calvin’s favorite cereal, Chocolate Frosted Sugar Bombs, come with a prize at the bottom of the box. The chance that the prize is a secret decoder ring is 10%. Calvin really wants one, so he borrows his Dad’s credit card and orders 80 boxes on-line. When the shipment arrives, Calvin opens all 80 boxes and finds 11 secret decoder rings. Use the Standard Normal Probability and the Inverse Normal tables to answer the questions. (Round percents to the nearest .01%)

1. What is the population proportion?
2. What proportion of the 80 boxes are expected to contain secret decoder rings?
3. What proportion of the boxes are expected not to contain secret decoder rings?
4. How many of the boxes are expected to contain secret decoder rings?
5. How many of the boxes are expected not to contain secret decoder rings?
6. What sample proportion did Calvin find?
7. What is the probability of getting a sample proportion at least as high as what Calvin got?
8. Of all the possible samples of 80 boxes, the middle 90% have sample proportions between  and  .

Answer 1

(there are more than 4 parts, as per policy i am answering first 4 parts)

a.

given : The chance that the prize is a secret decoder ring is 10%.

so, population proportion = p = 0.10

b.

expected proportion that contain = p = 0.10

c.

expected proportion that don't contain = 1-p = 0.90

d.

Expected to contain = n*p

= 80*0.10

= 8

e.

expected to not contain = n*(1-p)

= 80*(1-0.10)

= 72

(please upvote)