(a)
To find: the probability that the 8th one tested is the first vitamin D-deficient child.
(a)
Answer to Problem 36E
0.419
Explanation of Solution
Given:
The probability that a British child is vitamin D deficient = 0.2
Let X is the number of children tested to find the first child deficient in vitamin D.
Calculation:
Required probability is
There is a 4.2 probability that the 8th one checked was the first vitamin D deficient child.
(b)
To find: the chance that the first 10 kids tested are all good.
(b)
Answer to Problem 36E
10.73
Explanation of Solution
Given:
The probability that a British child is vitamin D deficient = 0.2
Let X is the number of children tested to find the first child deficient in vitamin D.
Calculation:
Required probability is
Hence there is 10.73% possibility that all children are okay.
(c)
To find: number of children do they supposed to test before finding one who has this vitamin deficiency.
(c)
Answer to Problem 36E
5
Explanation of Solution
Given:
The probability that a British child is vitamin D deficient = 0.2
Let X is the number of children tested to find the first child deficient in vitamin D.
Calculation:
Expected number is
Therefore, before finding a child who is defective, five children should be tested.
(d)
To find: the mean and standard deviation of the amount that may be vitamin D deficient.
(d)
Answer to Problem 36E
Mean = 10
Standard deviation = 2.83
Explanation of Solution
Given:
The probability that a British child is vitamin D deficient = 0.2
Let X is the number of children tested to find the first child deficient in vitamin D.
Formula used:
Calculation:
Standard deviation is
Therefore, Mean is 10 and Standard deviation is 2.83.
(e)
To find: the probability that vitamin deficiency is present in not more than fifty of them.
(e)
Explanation of Solution
Given:
Calculation:
Let X be number of children who are deficient. Were n = 320
The number of children tested is less than 10% of all children
Hence can approximate binomial distribution to normal
Hence X is normal (64, 7.16)
The probability that no more than 50 they are deficient is
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