Answer:
B. This statement is false. A true statement is, "As the size of a sample increases, the standard deviation of the distribution of sample means decreases
Step-by-step explanation:
Standard deviation of distribution of sample means =
Sample size = n
Population standard deviation =
The formula to calculate the standard deviation of distribution of sample means is:
From the above relation we can see that:
Standard deviation of the distribution of sample means is inversely related to the sample size. In inverse relation if one quantity increases the other will decrease. So, if the size of the sample is increased, the standard deviation of the distribution of sample means will Decrease.
Hence, the given statement is False. Therefore, the correct answer will be:
B. This statement is false. A true statement is, "As the size of a sample increases, the standard deviation of the distribution of sample means decreases"
(2n-4)-(4n-3)
=2n-4-4n+3
=-2n-1
=-(2n+1)
Answer:
0.8413 or 84.13%
Step-by-step explanation:
Given : The mean is 72 inches and the standard deviation is 15 inches
To Find : What is the probability that in a randomly selected year, the snowfall was less than 87 inches
Solution:
Mean =
Standard deviation =
Formula :
We are supposed to find the probability that in a randomly selected year, the snowfall was less than 87 inches
So, x = 87
Substitute the values in the formula
Now to find P(z<87) refer the z table
P(Z<87)=0.8413 = 84.13%
So, the probability that in a randomly selected year, the snowfall was less than 87 inches if the mean is 72 inches and the standard deviation is 15 inches is 0.8413 or 84.13%