Question

In: Statistics and Probability

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

  1. 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
  1. Find the probability that this diabetic eats at least 3 meals in a day.

  2. Find the expected number of meals that the diabetic eats in a day.

  3. 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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