Data are drawn from a bell-shaped distribution with a mean of 25 and a standard deviation of 4. There are 1.000 observations in the data set.
a. Approximately what percentage of the observations are less than 33? (Round your answer to 1 decimal place.)
b. Approximately how many observations are less than 33?

a) 97.7%

b) Approximately 977 of these observations are less than 33.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

a. Approximately what percentage of the observations are less than 33? (Round your answer to 1 decimal place.)

This is the pvalue of Z when X = 33. So

has a pvalue of 0.977

So 97.7% of the observations are less than 33.

b. Approximately how many observations are less than 33?

97.7% of 1000. So

0.977*100 = 977.

Approximately 977 of these observations are less than 33.

seems like d

step-by-step explanation:

1. 3.4/4

2. 0.8/7

3. 0.5 x 3

4. 0.9 x 6

5. 10.8

6. 2.35

7. 0.567

8. 9.35

9. 0.02

10. 0.06

11. 0.16

12. 0.42

13. 0.63

14. 5.6

15. 8.1

16. 9.9

17. 0.28

18. 0.48

19. 0.27

20. 0.49

21. 0.45

22. 0.72

23. 0.9

24. 0.88

25. 0.75

26. 0.16

27. 0.328

28. 0.495

29. 0.72

30. 1.068