1. A supply company currently sells a certain chemical to customers in large bar

Question

1. A supply company currently sells a certain chemical to customers in large barrels. Let X = “the number of barrels ordered by a randomly chosen customer.” Suppose that X has probability distribution

x 1 2 3 4

f(x) 0.2 0.4 0.3 0.1

µ = E(X) = your answer to part (b)

2 = V ar(X) = 0.81

(a) What is the probability that the number of barrels purchased is less than or equal to 2?

(b) Find the mean number of barrels purchased: µ = E(X).

(c) Find the mean and standard deviation of the sample mean (X) for n = 36 randomly selected customers.

(d) Approximate the probability that the sample mean number of barrels for n = 36 customers will be less than or equal to 2.

(e) Which probability is smaller, the one in part (a) or the one in part (d)? Circle one choice and explain why this makes sense.

Explanation / Answer

a) probability that the number of barrels purchased is less than or equal to 2 =P(X<=2) =0.2+0.4 =0.6

b)

E(X) =2.30

c)mean for n = 36 is 2.30

and std deviation =/(n)1/2 =0.9/(36)1/2 =0.15

d)

e)

probability is smaller the one in part (d)

x p(x) xP(x) (x-)2 (x-)2P(x) 1 0.200 0.200 1.690 0.338 2 0.400 0.800 0.090 0.036 3 0.300 0.900 0.490 0.147 4 0.100 0.400 2.890 0.289 total 1 = 2.30 5.160 2= 0.8100 std deviation=     =    2 = 0.9000

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