Question

The number x of bottles of garden plant fungicide sold by a garden center each day was

recorded with the following results:

? 0 1 2 3 4 5 6 7

?(?) 0.135 0.141 0.150 p 0.134 0.122 0.101 0.074

a. Find the value of p in the table.

b. Find the probability that at most two bottles will be sold on a randomly selected

day.

c. Find the probability that at least two bottles will be sold on a randomly selected

day.

d. Find the average number of bottles sold per day.

e. Find the standard deviation of the number of bottles sold per day

Answer 1

Solution :

a) Sum of all probabilities must be equal to one. Hence,

0.135 + 0.141 + 0.150 + p + 0.134 + 0.122 + 0.101 + 0.074 = 1

0.857 + p = 1

p = 1 - 0.857

p = 0.143

b) We have to find P(X ≤ 2).

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

P(X ≤ 2) = 0.135 + 0.141 + 0.150

P(X ≤ 2) = 0.426

Hence, the probability that at most two bottles will be sold on a randomly selected day is 0.426.

c) We have to find P(X ≥ 2).

P(X ≥ 2) = 1 - P(X < 2)

P(X ≥ 2) = 1 - [P(X = 0) + P(X = 1)]

P(X ≥ 2) = 1 - [0.135 + 0.141]

P(X ≥ 2) = 1 - 0.276

P(X ≥ 2) = 0.724

Hence, the probability that at least two bottles will be sold on a randomly selected day is 0.724.

d) The average for a discrete random variable is given by,

The average number of bottles sold per day is 3.14.

e) The standard deviation is given as follows :

We have, E(X) = 3.14

Now,

The standard deviation of the number of bottles sold per day is 2.1504.

Please rate the answer. Thank you.