Question

In: Statistics and Probability

1. To construct a particular binomial probability, it is necessary to know the total number of...

1. To construct a particular binomial probability, it is necessary to know the total number of trials and the probability of success on each trial. TRUE OR FALSE

2. The mean of a binomial distribution can be computed in a "shortcut" fashion by multiplying n (the total number of trials) times π (the probability of success). TRUE OR FALSE

3. Judging from recent experience, 5% of the computer keyboards produced by an automatic, high-speed machine are defective. If six keyboards are randomly selected, what is the probability that none of the keyboards are defective?

4. On a very hot summer day, 5% of the production employees at Midland States Steel are absent from work. The production employees are randomly selected for a special in-depth study on absenteeism. What is the probability of randomly selecting 10 production employees on a hot summer day and finding that none of them are absent?

5. Which one of the following is NOT a condition of the binomial distribution?

Multiple Choice

A. Independent trials.

B. Only two outcomes.

C. The probability of success remains constant from trial to trial.

D. Sampling at least 10 trials.

Solutions

Expert Solution

(1) It is true because we need the total number of trials n and probability p to find out any binomial probability. therefore this statement is true.

(2) True, because the formula for the mean of binomial distribution is given mean = n*p, where n is total trials and p is probability.

(3) it is given that p = 5% = 5/100 = 0.05

number of trials = 6

we have to find the probability that exactly 0 defective keyboard is there

Using the binomial formula

P(exactly 0)=

setting n =6 and r= 0, p = 0.05

we get

P(exactly 0)=

this gives

P(exactly 0)= 0.7351

(4)it is given that p = 5% = 5/100 = 0.05

number of trials = 10

we have to find the probability that exactly 0 absent is there

Using the binomial formula

P(exactly 0)=

setting n =10 and r= 0, p = 0.05

we get

P(exactly 0)=

this gives

P(exactly 0)= 0.5987

(5) Option A, B and C are compulsory conditions for binomial distribution, but having at least 10 trials is not any condition for binomial distribution.

So, option D is correct answer.

orchestra answered 2 years ago
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