I have to put this assignment in excel. Just want to make sure it\'s correct or
ID: 2840666 • Letter: I
Question
I have to put this assignment in excel. Just want to make sure it's correct or not. Please help!! This is what I have,
The weight of male students at a certain university is normally distributed with a mean of 168 pounds with a standard deviation of 8.6 pounds.
i) What is the probability that a male student weighs at most 174 pounds?
=NORM.DIST(174,168,8.6,TRUE)
ii) What is the probability that a male student weighs at least 165 pounds?
= 1- NORM.DIST(165,168,8.6,TRUE)
iii) What is the probability that a male student weighs between 170 and 190 pounds?
=NORM.DIST (190,168,8.6, TRUE) - =NORM.DIST(170,168,8.6,TRUE)
Explanation / Answer
Your answers to 1 and 2 are correct.
On 3, you just remove the second = sign and the blank before the first parentheses
To see that the answers are reasonable, the answer on 1 is 0.757309585103178
The probability of being at or below the mean of 168 is .5
Then, as the standard deviation is 8.6, and 8.6+168 = 176.8, 174 is less than 1 standard deviation above the mean.
The probability of being between the mean and 1 standard deviation above it is .34.
.34 + .5 = .84
The answer, .757, is between .5 and .84, so it is reasonable.
The answer on 2 is 0.636394236489876
To get the probability of being at least 165 pounds, as the mean is 168, this includes the probability of being above the mean is .5
Then, 168 - 8.6 = 159.4, so 165 is within 1 standard deviation of the mean, so again, the probability is less than .5+.34 = .84, so it is between .5 and .84
Note that 165 is within 3 of the mean, while 174 is 6 from the mean, so it makes sense that the answer on 1 is greater than the answer on 2.
For 3, the answer is 0.402790575078334
notice that 170 and 190 are both above the mean, so the probability is less than .5
190 is 22 above the mean, and this is 22/8.6 = 2.55 standard deviations above the mean. Thus, since 170 is 2 above the mean, which is 2/8.6 = .23 standard deviations, it makes sense for the probability to be .4 for the probability to be close to .5 but not too close, especially as 170 is almost 1/4 standard deviation above the mean.