Can someone please show me how to solve this. Your help is greatly appreciated.

Question

A study found that 25% of the bottled water from different brands is not safe to drink.

Suppose a researcher randomly selects 20 bottled water from different brands. let x is the

number of bottled water from different brands which is not safe to drink.

a. Explain why x is a binomial random variable. [2 Marks]

b. What is the probability that at least one bottled water is not safe to drink? [2 Marks]

c. What is the probability that exactly 18 bottled water is safe to drink? [2 Marks]

d. Find P(x < 2). Interpret the result. [2+1=3 Marks]

e. What is the average no. of bottled water which is not safe to drink?

Answer 1

requirements for binomial

a)

B = binary outcome - safe or not safe

I = independent - each bottle of water independent

N = fixed number of samples (20)

S = same probability of unsafe (0.25)

binomial probability formula

C(n,x) p^x (1-p)^n-x, where n is number of samples, x is number of not safe and p is probability of success. for this study, n = 20, p = 0.25, C(n,x) is number of combinations n taken x at a time

b) compute 1 - probability (zero not safe to drink), where latter probability is found using binomial formula for x = 0

c) use binomial formula for x = 18.

d) use binomial formula for x = 0 and x = 1 then add probabilities

e) expected value for binomial is np