A manufacturer knows that their items have a normally distributed length, with a mean of 16.2 inches, and standard deviation of 0.9 inches. If one item is chosen at random, what is the probability that it is less than 16.4 inches long

57.926%

Step-by-step explanation:

Calculation for the probability that it is less than

16.4 inches long

Using this formula

z = (X - μ) / σ

Where,

X represent Date=16.4

μ represent Mean=16.2

σ represent Standard deviation=0.9 inches

Let plug in the formula

z = (16.4 - 16.2) /0.9 inches

z=0.2/0.9 inches

z = 0.2

Using Z-score table to find the area of 0.2

z=0.57926*100

z=57.926%

Therefore the probability that it is less than

16.4 inches long is 57.926%

47 - 90 = 43

43 - 180 = x

x = 137