Question

question
when isabella goes bowling, her scores are normally distributed with a mean of 160 and standard deviation of 13. out of the 120 games that she bowled last year, how many of them would she be expected to score less than 155, to the nearest whole number?
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Explanation:

Step1: Calculate z-score

The z-score formula is $z = \frac{x - \mu}{\sigma}$, where $x=155$, $\mu=180$, $\sigma=13$.
$z = \frac{155 - 180}{13} = \frac{-25}{13} \approx -1.923$

Step2: Find cumulative probability

Look up $z \approx -1.92$ in the standard normal table or use a calculator to find the cumulative probability $P(Z < -1.923) \approx 0.0274$

Step3: Calculate expected number

Multiply the probability by total games (120).
$\text{Expected number} = 120 \times 0.0274 \approx 3.288$

Answer:

3