Answer:
98.77%
Explanation:
The probability that a randomly chosen item from the manufacturer’s items has a length less than 10.5 inches can be calculated using the cumulative distribution function (CDF) of the normal distribution. The CDF gives the probability that a random variable is less than or equal to a certain value.
The mean length of the items is 6.7 inches and the standard deviation is 1.7 inches 1. Let X be the length of a randomly chosen item. Then X ~ N(6.7, 1.7^2) 1. We want to find P(X < 10.5).
Using the standard normal distribution, we can standardize X as follows:
Z=σX−μ=1.710.5−6.7=2.2353
Then, we can use a standard normal distribution table or calculator to find that P(Z < 2.2353) is approximately 0.9877 1. Therefore, the probability that a randomly chosen item has a length less than 10.5 inches is approximately 98.77%.