Of those people who lose weight on a diet, 90% gain all the weight back. In a random sample of 12 dieters who have lost weight, what is the probability of each of the following?

From 8 to 10 gain the weight back, including 8 and 10

a 0.118

b. 0.085

c. 0.336

d. 0.387

e. 1.17

f. Not here

The correct answer is C. 0.336

It means that there is a probability of 33.6% that 8 to 10 dieters out of 12 of this random sample, gained the weight back after losing weight on a diet.

Step-by-step explanation:

1. Let's review the information provided to us to answer the problem correctly:

Probability of gaining weight back after losing weight on a diet = 90% = 0.9

Random sample = 12 dieters

2. What is the probability of each of the following? From 8 to 10 gain the weight back, including 8 and 10.

This is a binomial distribution and we will use the following table to answer the question, with P = 0.9 and 12 trials is:

P (0) = 1.0E-12

P (1) = 1.08E-10

P (2) = 5.346E-9

P (3) = 1.6038E-7

P (4) = 3.247695E-6

P (5) = 4.6766808E-5

P (6) = 0.000491051484

P (7) = 0.003788111448

P (8) = 0.021308126895

P (9) = 0.08523250758

P (10) = 0.230127770466

P (11) = 0.376572715308

P (12) = 0.282429536481

Now, we can calculate the answer this way:

P (8) + P (9) + P (10)

0.0213 + 0.0852 + 0.2301 = 0.3366

The correct answer is C. 0.336

It means that there is a probability of 33.6% that 8 to 10 dieters out of 12 of this random sample, gained the weight back after losing weight on a diet.