(a) Use the frequency distribution to construct a probability distribution. (b) Graph the probability distribution using a histogram and describe its shape. (c) Find the mean, variance, and standard deviation of the probability distribution. (d) Interpret the results in the context of the real life situation.

x = the number of
defects per batch of camping chairs inspected.

(a) Construct a probability distribution.

It is given that
Defects 0 1 2 3 45
Batches 95 113 87 64 13 8
The sum of the second row is 380. Divide each number in the second row by 380 and relabel
the rows as follows:
x 012345
P (x) .250 .297 .229 .168 .034 .021

That is, if we choose at random one of the 380 batches of chairs, the probability that batch has
x = 0 defects is 0.250.

(c) We calculate the mean, variance, and standard deviation. We enter the probability distribution
into two lists.
L1 012345
L2 .250 .297 .229 .168 .034 .021
Now, entering 1-Var Stats L1,L2, we see that μ = 1.5, σ2
x ≈ 1.54, σx ≈ 1.24 . (The value of σ2
x
was obtained squaring the value of σx.)