Question

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in a recent year, the scores for the reading portion of a test were normally distributed, with a mean of 22.5 and a standard deviation of 6.6. complete parts (a) through (d) below. (a) find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than 16. the probability of a student scoring less than 16 is . (round to four decimal places as needed.)

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 16$, $\mu=22.5$, and $\sigma = 6.6$. So, $z=\frac{16 - 22.5}{6.6}=\frac{- 6.5}{6.6}\approx - 0.9848$.

Step2: Find the probability

We want to find $P(X<16)$, which is equivalent to $P(Z < - 0.9848)$ using the standard normal distribution table. Looking up the value in the standard - normal table, we find that $P(Z < - 0.9848)\approx0.1623$.

Answer:

$0.1623$