(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:
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.
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
was obtained squaring the value of σx.)