What proportion of women in this age range are overweight according to this definition?

Question

a study suggested that women between ages 20 and 29 in the US have a mean BMI of 26.8 and standard deviation of 7.4

(lets assume these BMIs are normally distributed)

 

a BMI of 30 or greater is considered being overweight

Answer 1

x = 30
μ = 26.8
σ = 7.4

P(X ≥ x) = 1 - P[(X-μ)/σ < (x-μ)/σ]

P(X ≥ 30) = 1 - P[Z < (30-26.8)/7.4] = 1 - P(Z < 0.43)

From the table of normal distribution for z = 0.43, we get 0.666402.

So, 1 - 0.666402 = 0.333598