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SVETLANKA909090 [29]
1 year ago
5

The first National Health and Nutrition Exam Survey reported that the average body mass index(BMI) in the 25 to 39 age group for

women was found to be 24 with a standard deviation of 5. If awoman from this age group is selected at random, what is the probability she has a BMI between 32and 35.Write your probability as a decimal rounded to the nearest ten-thousandth.
Mathematics
1 answer:
Elena L [17]1 year ago
5 0

the average body mass index (BMI) in the 25 to 39 age group for women was found to be 24 with a standard deviation of 5

From the above, we can obtain this information:

mean: μ = 24

standard deviation: σ = 5

Question

a woman from this age group is selected at random, what is the probability she has a BMI between 32 and 35.

P ( 32

In order to find P ( 32

First, we need to calculate z-value

Z=\frac{x-\mu}{\sigma}

P(x<35)

Z=\frac{35-24}{5}=2.2

now, we can use a Z-score table to find the probability having the above z-value of 2.2

P(z<2.2) = 0.9861

Therefore, P(x<35) = 0.9861

P(x<32)

Z=\frac{32-24}{5}=1.6

Again, using the Z-score table, for a value of Z=1.6, the probability is

P(z<1.6) = 0.9452

Therefore, P(x<32) = 0.9452

Finally, we must solve P(x<35) - P(x<25) to find P(32this is: 0.9861 - 0.9452 = 0.0409

Which is the same as: P(1.6or P(32

In conclusion, the probability of selecting a woman with an IBM between 32 and 35 is P = 0.0409

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