In: Statistics and Probability
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.
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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