A manager of restaurant knows that 30% of his customers are professional trucker
ID: 3202985 • Letter: A
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
Yes. It meets the condition of binomial distribution:
1: The number of observations n is fixed.
Yes,12
2: Each observation is independent.
Yes, it' independent
3: Each observation represents one of two outcomes ("success" or "failure").
Yes, the driver is either professional or not.
4: The probability of "success" p is the same for each outcome.
p is same i.e. .30 in out case
The RV is the no. of truck drivers that are professional
What is the probability that exactly 4 are truck drivers?
P(X=4) = 12C4(.3^4)(.7^8) = .23114
What is the probability that 5 or fewer are truck drivers?
=P(X=0)+..P(X=5) = 0.8821
What is the probability that at least 4 are truck drivers?
P(X>=4) = 0.5075
What is the probability that at most 4 are truck drivers?
P(X<4) = 0.4925
Mean in binomial dist is np = 12*.3 = 3.6
Stdev in binomial dist is npq = 12*.3*.7 = 3.6*.7 = 2.52
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