Question

test 3
score: 0.75/6 answered: 1/6
question 2
a manufacturer knows that their items have a normally distributed length, with a mean of 15.7 inches, and standard deviation of 4.1 inches.
if one item is chosen at random, what is the probability that it is less than 26.5 inches long?
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Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x = 26.5\), \(\mu=15.7\), and \(\sigma = 4.1\).

$$ z=\frac{26.5 - 15.7}{4.1}=\frac{10.8}{4.1}\approx2.63 $$

Step2: Find the probability using the standard normal distribution

We want to find \(P(X\lt26.5)\), which is equivalent to \(P(Z\lt2.63)\) in the standard normal distribution.
Looking up the value of \(z = 2.63\) in the standard - normal table (or using a calculator with a normal - distribution function, e.g., for a TI - 84: normalcdf(-100,2.63)), we get \(P(Z\lt2.63)\approx0.9957\)

Answer:

\(0.9957\)