Question

Determine the following probabilities. a. For n=5 and x=0.19, what is P(x=0) ? b. For n=11 and t=0.50, what is P(X=10) ? c. For n=11 and π=0.60, what is P(X=9) ? d. For n=2 and π=0.87, what is P(X=1)? a. When n=5 and π=0.19,P(X=0)=.3487. (Round to four decimal places as needed) b. When n=11 and π=0.50,P(X=10)= (Round to four decimal places as needed)

Answer 1

To find the probabilities, you can use the binomial probability formula. For part a, with n=5 and x=0.19, P(x=0) is 0.624032. For part b, with n=11 and t=0.50, P(X=10) is 0.005371094.

Step-by-step explanation:

a. For n=5 and x=0.19, what is P(x=0) ?

To determine the probability P(x=0), we can use the binomial probability formula:

P(x=k) = (n choose k) * p^k * q^(n-k)

where n is the number of trials, k is the number of successes (in this case, 0), p is the probability of success, and q is the probability of failure (1-p).

Filling in the values, we have:

P(x=0) = (5 choose 0) * (0.19)^0 * (1-0.19)^(5-0) = 1 * 1 * 0.624032 = 0.624032

b. For n=11 and t=0.50, what is P(X=10) ?

To determine the probability P(X=10), we can again use the binomial probability formula:

P(X=k) = (n choose k) * p^k * q^(n-k)

Filling in the values, we have:

P(X=10) = (11 choose 10) * (0.50)^10 * (1-0.50)^(11-10) = 11 * 0.000976563 * 0.5

= 0.005371094