alexs times for running a mile are normally distributed with a mean time of 5.28 minutes and a standard…

alexs times for running a mile are normally distributed with a mean time of 5.28 minutes and a standard deviation of 0.38 seconds. chriss times for running a mile are normally distributed with a mean time of 5.45 seconds and a standard deviation of 0.2 seconds. ten of alexs times and 15 of chriss times are randomly selected. let $\bar{x}_a-\bar{x}_c$ represent the difference in the mean times for alex and chris. which of the following represents the mean of the sampling distribution for $\bar{x}_a - \bar{x}_c$?\n-0.17\n0.17\n-0.18\n0.18

alexs times for running a mile are normally distributed with a mean time of 5.28 minutes and a standard deviation of 0.38 seconds. chriss times for running a mile are normally distributed with a mean time of 5.45 seconds and a standard deviation of 0.2 seconds. ten of alexs times and 15 of chriss times are randomly selected. let $\bar{x}_a-\bar{x}_c$ represent the difference in the mean times for alex and chris. which of the following represents the mean of the sampling distribution for $\bar{x}_a - \bar{x}_c$?\n-0.17\n0.17\n-0.18\n0.18

Answer

Explanation:

Step1: Recall the property of the mean of the difference of two - sample means

The mean of the sampling distribution of $\bar{x}_A-\bar{x}C$ is given by $\mu{\bar{x}_A - \bar{x}_C}=\mu_A-\mu_C$, where $\mu_A$ is the population mean of Alex's times and $\mu_C$ is the population mean of Chris's times.

Step2: Identify the population means

We are given that $\mu_A = 5.28$ minutes. First, convert it to seconds. Since 1 minute = 60 seconds, $\mu_A=5.28\times60 = 316.8$ seconds. And $\mu_C = 5.45$ seconds.

Step3: Calculate the mean of the sampling distribution

$\mu_{\bar{x}_A-\bar{x}C}=\mu_A - \mu_C=316.8 - 5.45=311.35$ (There is a unit - error in the problem statement as the means are given in different units. Assuming both are in seconds, if we correct the problem and assume $\mu_A = 5.28$ seconds) $\mu{\bar{x}_A-\bar{x}_C}=\mu_A-\mu_C=5.28 - 5.45=- 0.17$ seconds.

Answer:

A. -0.17