Question

A particular brand of tablet comes in two models, one with 16 GB and the other with 32 GB. The 32 GB model is more populuar, 70% of consumers who want to buy this tablet want this model. (a) Among 20 randomly selected consumers who want to buy this tablet, what is the probability that exactly 11 want the 32 GB model?

Answer 1

To find the probability that exactly 11 out of 20 randomly selected consumers want the 32 GB model of the tablet, you can use the binomial probability formula. The probability is approximately 0.2133 (or 21.33%).

Step-by-step explanation:

To find the probability that exactly 11 out of 20 randomly selected consumers want the 32 GB model of the tablet, we can use the binomial probability formula. In this case, the probability of success (p) is 0.7, since 70% of consumers want the 32 GB model. The total number of trials (n) is 20.

The binomial probability formula is:

P(X=k) = C(n,k) * p^k * (1-p)^(n-k)

where C(n,k) represents the number of combinations of n items taken k at a time.

Using this formula, we can calculate the probability as:

P(X=11) = C(20,11) * 0.7^11 * (1-0.7)^(20-11).

Calculating the values gives us:

P(X=11) = 167960 * 0.7^11 * 0.3^9 ≈ 0.2133.

Therefore, the probability that exactly 11 out of 20 randomly selected consumers want the 32 GB model is approximately 0.2133 (or 21.33%).