Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is less than negative 0.93 and draw a sketch of the region.

Step-by-step explanation:

We can solve this question taking into account the concepts of the standard normal distribution and the z-scores. We can say that the former is a special normal distribution from which we can obtain probabilities for all normally distributed data. Likewise, the z-scores are "transformed" values for raw scores, and we can use them to find probabilities using the standard normal distribution.

The question tells us something important "Those test scores are normally distributed with a mean of 0 and a standard deviation of 1".

Thus, it refers to the standard normal distribution. In this distribution, every given score is a z-score. A z-score tells us the distance from the mean in standard deviation units. Moreover, a negative score means that the value is below the mean, whereas a positive score tells us that the value is above the mean in the distribution.

Well, we have to find the probability that "a given score is less than negative 0.93", that is z = -0.93.

With the help of a standard normal table, we can find this probability using z = -0.93 as an entry to the table to find it. However, in most tables of this kind, we have positive values for z-scores. Fortunately, the standard normal distribution, as well as the normal distribution, is symmetrical and we can verify that:

Then, the probability is as follows:

That is, "the probability that a given score is less than negative 0.93" is 0.17619 or .

We can see that the graph below represents this region. It is below the mean (at the left hand from the population mean, at 0.93 standard deviation units, and it represents an area that is, approximately, 17.619% of the total area of the standard distribution).

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

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