Question 1: 41% of postmenopausal women have low bone density (osteopenia), plac

Question

Question 1:

41% of postmenopausal women have low bone density (osteopenia), placing them at risk for osteoporosis with ensuing spontaneous fractures. Osteoporosis is estimated to cost $14 billion per year in medical expenses alone, and yet it can be prevented if treated early enough. A physicians group has 247 postmenopausal primary patients and has diagnosed 83 with low bone density.

(a) Find the probability that only 83 or fewer of the 247 patients have low bone density [hint: use the Normal approximation to the binomial distribution]. _____________ (Use 4 decimal places.)

(b) Based on your answer, what would you suggest at the next physicians meeting?

-The diagnosis of the 83 patients is consistent with expectations, and no change is needed.

-Because of the high cumulative probability for 83 patients or fewer, it is likely that cases of osteopenia have been misdiagnosed (too many diagnosed).     

-Because of the low cumulative probability for 83 patients or fewer, it is likely that cases of osteopenia have been missed (not diagnosed).

-No conclusions can be drawn. A larger sample is needed.

Question 2:

Each newborn baby has a probability of approximately 0.49 of being female and 0.51 of being male. For a family with four children, let X = the number of children who are girls.

(a) Which of the following conditions must be satisfied for X to have a binomial distribution? Select all that apply.

-Each birth results in one of two outcomes, boy or girl.

-The probability of having a girl is the same for each birth.

-The probability of having a boy is the same for each birth.

-The probability of having a girl or boy changes from birth to birth.

-The sex of one child has no bearing on the sex of the next child.

-The sex of one child affects the sex of the next child.

(b) Identify n and p for the binomial distribution.

n = ___________ p =__________

(c) The probability that the family has two girls and two boys is _________ . Use 3 decimal places.

Explanation / Answer

Solution:-

2)a)

- Each birth results in one of two outcomes, boy or girl.

-The probability of having a girl is the same for each birth.

-The probability of having a boy is the same for each birth.

-The sex of one child has no bearing on the sex of the next child.

b)

n = number of total children

n = 4

p = probability that children is female.

p = 0.49

c) The probability that the family has two girls and two boys is 0.375.

n = 4

p = 0.49

x = 2

By applying binomial distributiion:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x = 2) = 0.375

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