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Vinil7 [7]
3 years ago
10

A manufacturer knows that their items have a normally distributed length, with a mean of 8.8 inches, and standard deviation of 0

.7 inches.
If one item is chosen at random, what is the probability that it is less than 8.2 inches long?
Mathematics
1 answer:
Alex777 [14]3 years ago
6 0

Answer:

0.1949

Step-by-step explanation:

Given a normal distribution with;

Mean(m) = 8.8 inches

Standard deviation (sd) = 0.7 inches

If one item is chosen at random, what is the probability that it is less than 8.2 inches long?

Find the Z-score :

x = 8.2 inches

Z = (x - m) / sd

Zscore = (8.2 - 8.8) / 0.7

Zscore = - 0.6 / 0.7

Zscore = - 0.857 = - 0.86

P(Z < - 0.86) :

From z distribution table :

P(Z < - 0.86) = 0.1949

If one item is chosen at random, there is a probability of 0.1949 that it will be less than 8.2 inches long.

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