# The number x of bottles of gar

The number x of bottles of garden plant fungicide sold by agarden 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 soldon a randomly selected
day.
c. Find the probability that at least two bottles will be soldon a randomly selected
day.
d. Find the average number of bottles sold per day.
e. Find the standard deviation of the number of bottles soldper day

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 besold 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 besold 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 is3.14.

e) The standard deviation is given as follows :

We have, E(X) = 3.14

Now,

The standard deviation of the number of bottles sold perday is 2.1504.

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