I have a stats problem I need help with please. I have a population of human sku

Question

I have a stats problem I need help with please. I have a population of human skulls from the misssissippi river. The average length recorded is (u) is 22.6 mm, with a population Stan. Dev. Of 0.2 mm. Note -> I think I need to do a standard error calculation. But I'm not sure because my professor said I might not need to do one for this Calculation. A) how many standard deviations away from the mean is a skull that has a length of 24.7 mm? B) what is the probability of a randomly selecting a skull from the population and getting one that is 24.7 mm long or greater ? C) what is the porportion of the population has skulls 24.6 mm or smaller. D) if you had a population of 5000 skulls, how many of them would be 25.1 mm or greater in size ?? E) what porportion of the population has skulls less than 21.4 mm or greater than 23.8 mm??? I have a stats problem I need help with please. I have a population of human skulls from the misssissippi river. The average length recorded is (u) is 22.6 mm, with a population Stan. Dev. Of 0.2 mm. Note -> I think I need to do a standard error calculation. But I'm not sure because my professor said I might not need to do one for this Calculation. A) how many standard deviations away from the mean is a skull that has a length of 24.7 mm? B) what is the probability of a randomly selecting a skull from the population and getting one that is 24.7 mm long or greater ? C) what is the porportion of the population has skulls 24.6 mm or smaller. D) if you had a population of 5000 skulls, how many of them would be 25.1 mm or greater in size ?? E) what porportion of the population has skulls less than 21.4 mm or greater than 23.8 mm??? I have a population of human skulls from the misssissippi river. The average length recorded is (u) is 22.6 mm, with a population Stan. Dev. Of 0.2 mm. Note -> I think I need to do a standard error calculation. But I'm not sure because my professor said I might not need to do one for this Calculation. A) how many standard deviations away from the mean is a skull that has a length of 24.7 mm? B) what is the probability of a randomly selecting a skull from the population and getting one that is 24.7 mm long or greater ? C) what is the porportion of the population has skulls 24.6 mm or smaller. D) if you had a population of 5000 skulls, how many of them would be 25.1 mm or greater in size ?? E) what porportion of the population has skulls less than 21.4 mm or greater than 23.8 mm???

Explanation / Answer

A) Let 24.7 - 22.6 = 2.1

So that 2.1/0.2 = 10.5 times standard deviations away from the mean is a skull that has a length of 24.7 mm

B) We want to find P(X > 24.7) = 1 - P(X < 24.7)

Let's used excel to find normal probability

The general command to find less than normal probability in excel is "=NORMDIST(x,mean,standard_dev,cumulative)"

put x = 24.7, mean = 22.6, standard_dev = 0.2, and cumulative = TRUE

So we get P(X < 24.7) = "=NORMDIST(24.7,22.6,0.2,1)" = 1

So that P(X > 24.7) = 1 - 1 = 0

P(X > 24.7) = 0

This is the final answer of part B).

C) P(X < 24.6) = "=NORMDIST(24.6,22.6,0.2,1)" = 1

the proportion of the population has skulls 24.6 mm or smaller is 1*100 = 100%

D) First we need to find P(X > 25.1) = "=1-NORMDIST(25.1,22.6,0.2,1)" = 0

So that 5000* 0 = 0

So we don't get any one whose size is 25.1 mm or greater out of 5000 skulls.

E) We want to find P(X < 21.4) + P(X >23.8)

let P(X < 21.4) = "=NORMDIST(21.4,22.6,.2,1)" = 0.000000000986588

P(X > 23.8) = "=1-NORMDIST(23.8,22.6,.2,1)" = 0.000000000986588

P(X < 21.4) + P(X >23.8) = 0.00000000197318 = 0.000000197318%

Almost 0% of the population has skulls less than 21.4 mm or greater than 23.8 mm

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.