Question 1.) The random variable X, representing the number of items sold in a w

Question

Question 1.) The random variable X, representing the number of items sold in a week, has the following probability distribution:

Which of the three random variables has the smallest standard deviation?

X

Y

Z

All three random variables have the same standard deviation.

Question 2.) The random variable X, representing the number of items sold in a week, has the following probability distribution:

By the fourth day of a particular week, 3 items have already sold. What is the probability that there will be less than a total of 5 items sold during that week?

1.00

0.95

0.90

0.85

0.67

x 0 1 2 3 4 5 6 P(X = x) 0.10 0.20 0.40 0.15 0.05 0.05 0.05 Probabilty Probability Probability

Explanation / Answer

1) Since the data is symmetric is all cases, the mean will be the middle value, that is 3. In Y, we have maximum number of frequencies which is equal to the mean. So, the variance is least for the distribution Y.

2) P(less than 5 items sold | 3 or more items sold) = P(3 or more and less than 5 items sold) / P(3 or more items sold)

= P(3 or 4 items sold)/P(3 or more items sold)

= (0.15 + 0.05)/(0.15 + 0.05 + 0.05 + 0.05)

= 0.67

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