Question

1. P(z<-2.12)= ?

2. P(z=2.6)=?

3. P(z>-3)=?

4. P(z<-2.36)=?

5. p(z>-0.24)=?

6. P(-1.88<z<1.65)=?

7. The mean amount of sleep needed for adults is 509 minutes per night. If the standard deviation for adult sleepers is 47. What is the Z score associated with sleeping 556 minutes per night? Round your answer to the nearest thousandth.

8. The mean amount of sleep needed for adults is 502 minutes per night. If the standard deviation for adult sleepers is 43. What is the Z score associated with sleeping 360 minutes per night? Round your answer to the nearest thousandth.

9. The mean amount of sleep needed for adults is 503 minutes per night. If the standard deviation for adult sleepers is [s]. What is the Z score associated with sleeping 503 minutes per night?

10. A student has earned a score of 76%. The class average is 70% and the standard deviation is 4%. What proportion of the class scored higher than the student assuming the grades are distributed normally? Please round answer to the nearest thousandth.

11. The class average is 70% and the standard deviation is 4%. A student from the class earned a 60%. What proportion of the class scored higher than the student assuming the grades are distributed normally? Please round your answers to the nearest thousandth.

12. The class average is 70% and the standard deviation is 4%. What proportion of the students from that same class earned a score between 66% and 74%? Please round your answer to the nearest hundredth.

13. A student in the same class scored an 89%. What proportion of students in the class scored higher than the student? Please round your answer to the nearest thousandth.

14. A class has a average height of 68 inches and a standard deviation of 2 inches. What height do you need to be taller than 90% of the class? Please round your answer to the nearest thousandth.

15. A class has an average height of 68 inches and a standard deviation of 2 inches. What height do you need to be taller than, so that at least 20% of the class is shorter than you ( nearest 1/100 of an inch)? Please round your answer to the nearest hundredth of an inch.

16. Suppose the mean weight for a population of deer is 140 pounds with a standard deviation of 20 pounds. Assume the weights of the deer are approximately normally distributed and a deer weighing less than 110 pounds is considered malnourished. What proportion of the deer are malnourished. (nearest 1/1000)

17. If the average weight for cats is 12 pounds and the standard deviation is 2 pounds. How big would a cat need to be to be in the top10% of the populations size? How big would the cat need to be to be in the bottom quarter of the data.

18. Suppose the average weight for cats is 12 pounds and a cat weighted 15 pounds. He was also in the 97th percentile for weight. How big is one deviation.

19. If the mean height for a class is 68 inches with a standard deviation of 2 inches, which of the following would yield a positive z score?

A)68 inches

B) 2 inches

C) 75 inches

D) 65 inches

Answer 1

Note: Since you have posted a question with multiple sub-parts, we will solve first four subparts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved.

Solution:

1)

P(Z< -2.12) = ...?

This probability can be either found using standard normal table or excel function.

Using excel function, =NORMSDIST(-2.12)

P(Z< -2.12) = 0.0170

This probability can be shown in graph as,

2)

P(z=2.6)=...?

We know, z follows standard normal distribution. Therefore, it is continuous probability distribution and there is zero probability for exact data point in continuous distribution.

Hence, P(z=2.6)=0

3)

P(z> -3)= ...?

Using excel function, =1-NORMSDIST(-3)

Hence, P(z> -3)=0.9987

Graphically,

4)

P(z< -2.36)= ...?

Using excel function,  =NORMSDIST(-2.36)

P(z< -2.36)= 0.0019

Graphically,

Done