A manager of restaurant knows that 30% of his customers are professional trucker

Question

A manager of restaurant knows that 30% of his customers are professional truckers. The manager surveys the next 12 customers who come into the restaurant to determine if they are professional truck drivers or not.

Does this situation meet the binomial requirements? Why or why not?

Address the five conditions of a binomial distribution in the textbook. What is the random variable in this problem? (i.e., what does X represent and what values can it have?)

What is the probability that exactly 4 are truck drivers?

What is the probability that 5 or fewer are truck drivers?

What is the probability that at least 4 are truck drivers?

What is the probability that at most 4 are truck drivers?

What is the mean number of customers out of a sample of 12 that you would expect to be truck drivers?

What is the standard deviation of the distribution?

Explanation / Answer

Solution:-
1)Yes, this situation meet the binomial requirements.
Reason 1.Fixed number of trials.
Reason 2. There are 2 possible outcomes for each trial. (Truck Driver or Not a Truck Driver).
Reason 3. Probability of success is the same for each trial.
Reason 4. The trials are independent.
Reason 5. The random variable "X" represents the number of people who are found to in fact be truck drivers.

2) X is the number of truck drivers out of 12 people surveyed so X can take any integer value from 0 to 12

3) n=12 P=.30 x=4
P(X = 4) = binompdf(12,0.3,4)
= .2311396961 or .2311

4)n=12 P=.30 x=5
P(X 5) = binomcdf(12,0.3,5)
= .882151261 or .88

5) n=12 P=.30 x=3
P(At least 4 are truck drivers)
= P(X 4)
= 1- P(X 3)
= 1 - binomcdf(12,0.3,3)
= 1- 0.49252
= 0.50748

6) n=12 P=.30 x=4
P(X 4) = binomcdf(12,0.3,4)
= .7236554696 or .72

7) Mean = np = 12*0.3 = 3.6
Standard deviation = square root of (np(1-p))
= square root of (12*0.3*(1-0.3))
= 1.587450787

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.