Question

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.(a) What is the probability that exactly seven are retired people?(b) What is the probability that 10 or more are retired people?

Answer 1

Answer:

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;

$P(X=r) =\binom{n}{r}p^{r}(1-p)^{n-r} for x = 0,1,2,3,....$

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) = $\binom{25}{7}0.2^{7}(1-0.2)^{25-7}$

                   = $480700*0.2^{7}*0.8^{18}$ = 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.