Concept explainers
a.
Find the probability that the numbers of orders for small, medium and large drinks are 5, 7, and 8 respectively.
a.
Answer to Problem 15E
The probability that the numbers of orders for small, medium and large drinks are 5, 7, and 8 respectively is 0.0411.
Explanation of Solution
Given info:
Total number of orders selected at random for audit is 20. There is about 25% of drink orders are for a small drink, 35% for a medium and 40% for a large.
Calculation:
The random variables
Multinomial distribution:
If the random variables
Substitute
Thus, the probability that the numbers of orders for small, medium and large drinks are 5, 7, and 8 respectively is 0.0411.
b.
Find the probability that more than 10 orders are for large drinks.
b.
Answer to Problem 15E
The probability that more than 10 orders are for large drinks is 0.1275.
Explanation of Solution
Calculation:
If the random variables
Binomial distribution:
The probability of obtaining x successes in n independent trails of a binomial experiment is,
Where, p is the probability of success.
Substitute x as 11,12,13,14,15,16,17,18,19,20 and p as 0.4in the formula.
Thus, the probability that more than 10 orders are for large drinks is 0.1275.
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