The randomly selected subject is given bone density test which are normally distributed with mean =0 and standard deviation =1. It means bone density test score is standard normal variable.
The probability that a given score is less than 2.23
P(z < 2.23)
Using z score table to find probability below z=2.23
P(z < 2.23) = 0.9871
The probability that a given score is less than 2.23 is 0.9871
Answer:
Keiko got a better answer on the test on her second test, and you could compare these two ratios as they are written.
Step-by-step explanation:
First: Convert each of the scores into percentages:
How do you convert ratios to percentages? Well, first we have to convert the ratio to a decimal or a fraction. Let's convert it to a fraction. So, 19 out of 25 will become , and 17 out of 20 will become
. To convert a fraction to a percentage:
19 ÷ 25 = 0.76 AND 17 ÷ 20 = 0.85
0.76 x 100 = 76 AND 0.85 x 100 = 85
76% AND 85%
Now the two quantities are easier to compare. We can obviously see that 85% is bigger [and better] than 76%. So, the ratio that equals 85% - 17 out of 20 - is a better grade.
The second question was: Can you compare these two ratios as they are written? Explain why or why not.
Yes, you can compare these two ratios, just find the [positive] difference between the amount that she scored and the total number of scores that could be gained.
25 - 19 = 6
20 - 17 = 3
Since the equation with 20 and 17 in it has a smaller difference, it is most likely to have a greater value [because that means that Keiko got more right and less wrong, which means a greater mark which is also a greater quantity].
Thanks,
Topic: Quantity Relationships, Quantity Conversions