SOLUTION: In a survey of nursing students pursuing a master’s degree, 84 percent stated that they expect to be promoted to a higher position within one month after receiving the degree. If

Question 1134279: In a survey of nursing students pursuing a master’s degree, 84 percent stated that they expect to be promoted to a higher position within one month after receiving the degree. If this percentage holds for the entire population, find, for a sample of 20, the probability that the number expecting a promotion within a month after receiving their degree is:
a. Five b. At least six
c. No more than four d. Between five and eight, inclusive

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Use the Binomial Probability Formula
:
Probability (P) (k successes in n trials) = nCk * p^(k) * (1-p)^(n-k), where nCk = n!/(k! * (n-k)!), p is probability of success
:
For this problem, p = 0.84, n = 20
:
a) P (k = 5, n = 20) = 20C5 * (0.84)^5 * (1-0.84)^(20-5) = 0.000001
:
b) P (k > or = 6, n = 20) = 1 - (summation i = 0 to 5 of P(k = i, n = 20) = 0.999999
:
c) P (k < or = 4, n = 20) = summation i = 0 to 4 of P(k = i, n = 20) = 0.000001
:
d) P (5 < or = k < or = 8, n = 20) = summation i = 5 to 8 of P(k = i, n = 20) = 0.000012
:

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