For a diabetic, the number of meals and quantity of calories in a day are very...

For a diabetic, the number of meals and quantity of calories in a day are very important to monitor. A diabetic monitored the number of times he eats in a day but since he leads a busy schedule he cannot always eat appropriately. Let X represent a discrete random variable of the number of meals that this diabetic consumes in a day. The following represents the probability distribution of X:

X 1 2 3 4 5

P=(X=x) 0.10 0.12 0.50 0.25 0.03

Find the probability that this diabetic eats at least 3 meals in a day.
Find the expected number of meals that the diabetic eats in a day.
Find the standard deviation of the number of meals that the diabetic eats in a day.

Solutions

Expert Solution

Solution :

x	P(x)	x * P(x)	x² * P(x)
1	0.1	0.1	0.1
2	0.12	0.24	0.48
3	0.5	1.5	4.5
4	0.25	1	4
5	0.03	0.15	0.75
Sum	1	2.99	9.83

(1)

The probability that this diabetic eats at least 3 meals in a day= 0.5 + 0.25 + 0.03 = 0.78

(2)

Expected number = = X * P(X) = 2.99

(3)

Standard deviation =

=X ² * P(X) - ²

= 9.83 - 2.99²

= 0.94334

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orchestra answered 2 years ago

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Subjects

X	1	2	3	4	5
P=(X=x)	0.10	0.12	0.50	0.25	0.03