Question

question 26 (3 points) saved the time required to complete a task is normally distributed with a mean of μ = 50 minutes and a standard deviation of σ = 8 minutes. what is the probability that a randomly selected task takes between 40 and 55 minutes? round to four decimal places. 0.6284 a√ question 27 (3 points) a sample of 25 employees has a mean salary of $65,000 with a sample standard deviation of $8,000. calculate the 95% confidence interval for the true mean salary. (the critical t - value for df = 24 is 2.064). round to the nearest dollar and write the answer in the following format: (00000, 00000) a√

Explanation:

Step1: Recall confidence - interval formula

The formula for a confidence interval for the population mean when the population standard - deviation is unknown is $\bar{x}\pm t_{\alpha/2}\frac{s}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $t_{\alpha/2}$ is the critical t - value, $s$ is the sample standard deviation, and $n$ is the sample size.

Step2: Identify given values

We are given that $\bar{x} = 65000$, $t_{\alpha/2}=2.064$, $s = 8000$, and $n = 25$.

Step3: Calculate the margin of error

The margin of error $E=t_{\alpha/2}\frac{s}{\sqrt{n}}$. Substitute the values: $\sqrt{n}=\sqrt{25}=5$, $\frac{s}{\sqrt{n}}=\frac{8000}{5}=1600$, and $E = 2.064\times1600=3302.4$.

Step4: Calculate the lower and upper bounds of the confidence interval

The lower bound is $\bar{x}-E=65000 - 3302.4=61697.6\approx61698$.
The upper bound is $\bar{x}+E=65000 + 3302.4=68302.4\approx68302$.

Answer:

$(61698, 68302)$