Question

test 3
score: 1.75/6 answered: 2/6
question 3
a manufacturer knows that their items have a normally distributed lifespan, with a mean of 7.4 years, and standard deviation of 2 years.
if you randomly purchase one item, what is the probability it will last longer than 4 years?
enter an integer or decimal number, accurate to at least 3 decimal places more...
question help: video
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Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x = 4\), \(\mu=7.4\), and \(\sigma = 2\).

$$z=\frac{4 - 7.4}{2}=\frac{-3.4}{2}=-1.7$$

Step2: Find the probability

We want \(P(X>4)\). Since \(P(X>4)=1 - P(X\leq4)\), and from the standard normal table (or using a calculator with a normal - distribution function), \(P(Z\leq - 1.7)\) can be found.
Using a standard normal table or a calculator (e.g., for a TI - 84: normalcdf(-1E99, - 1.7,0,1)), \(P(Z\leq - 1.7)=0.0446\)
Then \(P(X>4)=1 - 0.0446 = 0.9554\)

Answer:

\(0.955\)