In a study by Peter D. Hart Research Associates for the Nasdaq Stock Market, it was determined that 20% of all stock investors are retired people. In addition, 40% of all U. S. adults invest in mutual funds. Suppose a random sample of 25 stock investors is taken What is the probability that fewer than 4 are retired people

a) 0.1108

(b) 0.0173

Step-by-step explanation:

We are given that 20% of all stock investors are retired people. A random sample of 25 stock investors is taken.

Firstly, the binomial probability is given by;

where, n = number of trails(samples) taken = 25

r = number of successes

p = probability of success and success in our question is % of

retired people i.e. 20%.

Let X = Number of people retired

(a) Probability that exactly seven are retired people = P(X = 7)

P(X = 7) =

= = 0.1108

(b) Probability that 10 or more are retired people = P(X >= 10)

P(X >= 10) = 1 - P(X <= 9)

Now, using binomial probability table, we find that P(X <= 9) is 0.98266 at n = 25, p = 0.2 and x= 9

So, P(X >= 10) = 1 - 0.98266 = 0.0173.