Question

the daily commute times for employees at a large law firm are normally distributed, with mean of 54 minutes and a standard deviation of 9 minutes. bobbys commute time is 54 minutes, lindsays commute time, when converted to a z - score, is - 0.1, and helens commute time is longer than 40% of employees at the law firm. who has the shortest commute time?
bobby
lindsay
helen
bobby, lindsay, and helen all have the same commute times.
this question cannot be answered without more information.
question 10
1 pts
resting heart rates for adult athletes, in beats per minute, follow a normal distribution. tatums resting heart rate is such that 75% of athletes have higher heart rates than she does. this means that tatums heart rate is approximately how many standard deviations away from the mean?
0.5
0.7
1.0
0.6
this question cannot be answered without knowing the mean and standard deviation of the distribution.

Explanation:

Question 1

Step1: Analyze Bobby's commute time

Bobby's commute time is equal to the mean ($\mu = 54$ minutes), so his z - score is $z_{Bobby}=0$ since $z=\frac{x-\mu}{\sigma}$ and $x = \mu$ gives $z = 0$.

Step2: Analyze Lindsay's commute time

Lindsay's z - score is $z_{Lindsay}=- 0.1$. A negative z - score means her commute time is less than the mean.

Step3: Analyze Helen's commute time

Helen's commute time is longer than 40% of employees. Looking up in the standard normal distribution table (z - table), the z - score corresponding to a cumulative probability of 0.4 is approximately $z_{Helen}\approx - 0.25$.

Step4: Compare z - scores

Since $-0.25<-0.1 < 0$, Helen has the most negative z - score, so Helen has the shortest commute time.

Question 2

Step1: Determine the cumulative probability for Tatum

If 75% of athletes have higher heart rates than Tatum, then the cumulative probability $P(Z < z)$ for Tatum is $1 - 0.75=0.25$.

Step2: Look up z - score in the z - table

Looking up the value 0.25 in the standard normal distribution table, the z - score corresponding to a cumulative probability of 0.25 is approximately $z\approx - 0.67$. So Tatum's heart rate is approximately 0.7 standard deviations away from the mean (rounding to one - decimal place).

Answer:

Question 1: C. Helen
Question 2: B. 0.7