Question

Q4. A random sample of size $n_1=16$ is selected from a normal population with a mean of 75 and a standard deviation of 8. A second random sample of size $n_2=9$ is taken from another normal population (independent to the previous population) with mean 70 and standard deviation 12. Let $\bar{X}_1$ and $\bar{X}_2$ be the sample means from the two samples, respectively. a) Find the mean and standard deviation for $\bar{X}_1$ and $\bar{X}_2$, respectively. b) Find the probability that $\bar{X}_1 - \bar{X}_2$ exceeds 4.

Name: q4 a random sample of size n116 is selected from a normal population with a mean of 75 and a standard deviation of 8 a second random sample of size n29 is taken from another normal populat 48206
Uploaded: 2023-07-04T12:49:18-08:00
Duration: 2 min 58 s
Channel: Ahmet Yavas
Description: q4 a random sample of size n116 is selected from a normal population with a mean of 75 and a standard deviation of 8 a second random sample of size n29 is taken from another normal populat 48206

          Q4. A random sample of size $n_1=16$ is selected from a normal population with a mean of 75 and a
standard deviation of 8. A second random sample of size $n_2=9$ is taken from another normal population
(independent to the previous population) with mean 70 and standard deviation 12. Let $\bar{X}_1$ and $\bar{X}_2$ be
the sample means from the two samples, respectively.
a) Find the mean and standard deviation for $\bar{X}_1$ and $\bar{X}_2$, respectively.
b) Find the probability that $\bar{X}_1 - \bar{X}_2$ exceeds 4.

q4 a random sample of size n116 is selected from a normal population with a mean of 75 and a standard deviation of 8 a second random sample of size n29 is taken from another normal populat 48206

Added by Phillip G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Ahmet Yavas

07/04/2023

Step 1

The standard deviation of the sample mean $\bar{X}_1$ is equal to the standard deviation of the population divided by the square root of the sample size, which is 8/sqrt(16) = 2. Show more…

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Q4. A random sample of size $n_1=16$ is selected from a normal population with a mean of 75 and a standard deviation of 8. A second random sample of size $n_2=9$ is taken from another normal population (independent to the previous population) with mean 70 and standard deviation 12. Let $\bar{X}_1$ and $\bar{X}_2$ be the sample means from the two samples, respectively. a) Find the mean and standard deviation for $\bar{X}_1$ and $\bar{X}_2$, respectively. b) Find the probability that $\bar{X}_1 - \bar{X}_2$ exceeds 4.