Question

normal distribution w/ population size
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question
when jason commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 55 minutes and a standard deviation of 5 minutes. out of the 239 days that jason commutes to work per year, how many times would his commute be shorter than 62 minutes, 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 $x=62$, $\mu=55$, $\sigma=5$.
$z=\frac{62-55}{5}=\frac{7}{5}=1.4$

Step2: Find cumulative probability

Look up $z=1.4$ in the standard normal distribution table, the cumulative probability $P(Z<1.4)=0.9192$.

Step3: Calculate number of commutes

Multiply the probability by total days: $239\times0.9192$
$239\times0.9192=219.6888$

Step4: Round to nearest whole number

Round $219.6888$ to the nearest integer.

Answer:

220