Question

question
when zachary commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 58 minutes and a standard deviation of 5 minutes. out of the 274 days that zachary commutes to work per year, how many times would his commute be between 64 and 68 minutes, to the nearest whole number?
statistics calculator

Explanation:

Step1: Calculate z-scores for 64 and 68

For $x=64$: $z_1=\frac{64-58}{5}=1.2$
For $x=68$: $z_2=\frac{68-58}{5}=2$

Step2: Find corresponding probabilities

Using standard normal table:
$P(Z<1.2)=0.8849$, $P(Z<2)=0.9772$

Step3: Calculate interval probability

$P(1.2

Step4: Multiply by total commute days

$274\times0.0923\approx25.29$

Answer:

25