Question

In: Statistics and Probability

According to the CDC, in 2017-2018, the prevalence of obesity among American adults was 42.4%. In...

According to the CDC, in 2017-2018, the prevalence of obesity among American adults was 42.4%. In a random sample of 80 adults, let ˆp be the proportion that meet the CDC definition of obese.

(a) Describe the sampling distribution of ˆp. Your answer should include the shape of the distribution (and why you can make this conclusion), the mean, and the standard deviation.

(b) What is the probability that ˆp is between .40 and .44.

Expert Solution

Solution :

Given that ,

p = 0.424

1 - p = 0.576

n = 80

a)

= p = 0.424

= (p*(1-p))/n = (0.424*0.576)/80 = 0.05525

N( , )

b)

P(0.40 < < 0.44 ) = P((0.40-0.424)/0.05525 ) < ( - ) / < (0.44-0.424) /0.05525 ) )

= P(-0.43 < z <0.29)

= P(z < 0.29) - P(z < -0.43)

= 0.6141 - 0.3336

= 0.2805

Probability = 0.2805

orchestra answered 2 years ago

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