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?

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.

x² + 11x + 18 < 0  

[-11 ± sqrt(121 - 72)]/2 = (-11 ± 7)/2  

solution: (-9, -2)

step-by-step explanation: