Question

select the correct answer. brittany uses a stopwatch to time how long it takes each day for her school bus to travel from her house to school. she finds that the times are distributed normally, with a mean of 21 minutes and a standard deviation of 2 minutes. if there are 180 school days each year, approximately how many times in brittanys four - year of high school will the school bus take more than 27 minutes to travel from brittanys house to school? a. 36 b. 4 c. 1 d. 18

Explanation:

Step1: Calculate z - score

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 27$ (the time we are interested in), $\mu=21$ (mean) and $\sigma = 2$ (standard deviation). So $z=\frac{27 - 21}{2}=\frac{6}{2}=3$.

Step2: Find the probability of $z>3$

Using the standard normal distribution table, the cumulative distribution function $\varPhi(3)\approx0.9987$. The probability of $z > 3$ is $P(Z>3)=1 - P(Z\leq3)=1 - 0.9987 = 0.0013$.

Step3: Calculate the number of days

There are 180 school - days each year and 4 years, so a total of $n = 180\times4=720$ school - days. The number of days the bus takes more than 27 minutes is $N=n\times P(Z > 3)=720\times0.0013\approx1$.

Answer:

C. 1