Why?
The first thing we need to do is find the area of the triangle, we can to that by subtracting the area of ABCD from ACBE, then, we can use the formulas to calculate the area for both triangle and rectangle to find "f" and "g".
Calculating we have:
Now, we can calculate "f" by using the formula to calculate the area of the triangle:
Now, finding "g" by using the formula to calculate the area of the rectangle, we have:
Hence, we have that:
Have a nice day!
Answer:
When sample size increases from n = 23 to n = 35, the mean of the distribution of sample means remains same but the standard deviation of the distribution of sample means decreases from 0.073 to 0.059.
Step-by-step explanation:
We are given the amounts of time employees at a large corporation work each day are normally distributed, with a mean of 7.5 hours and a standard deviation of 0.35 hour.
Random samples of size 23 and 35 are drawn from the population and the mean of each sample is determined.
Here, = population mean = 7.5 hours
= population standard deviation = 0.35 hour
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<u><em>Let </em></u><u><em> = sample mean</em></u>
(a) The random samples of size of n = 23 is drawn from the population;
So, mean of the distribution of sample means = = 7.5 hours
Standard deviation for the distribution of sample means is given by;
s = =
= 0.073
(b) The random samples of size of n = 35 is drawn from the population;
So, mean of the distribution of sample means = = 7.5 hours
Standard deviation for the distribution of sample means is given by;
s = =
= 0.059
(c) So, as we can see that when sample size increases from n = 23 to n = 35, the mean of the distribution of sample means remains same but the standard deviation of the distribution of sample means decreases from 0.073 to 0.059.