Question

Question 4: In many American families, both parents work outside the home, while children spend time at daycare centers or are cared for by other relatives. The mean amount of time fathers spend with their child(ren) 0-6 years old per day is 1.22 hours. Suppose this time distribution is approximately normal with standard deviation 0.60 hours, and suppose a father with a child 0-6 years old is randomly selected. a. What is the probability that the father spends at least 2 hours with his b. What is the probability that the father spends between 1 and 1.5 hours c. If the child sees his or her father for less than 2.5 hours per day, the child on any given day? with his child on any given day? parental bond is weakened. What is the probability that this special bond will be weakened on any given day?

Answer 1

a)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	1.22
std deviation   =σ=	0.6000

probability =

P(X>2)

=

P(Z>1.3)=

1-P(Z<1.3)=

1-0.9032=

0.0968

b)

probability =

P(1<X<1.5)

=

P(-0.37<Z<0.47)=

0.6808-0.3557=

0.3251

c)

probability =

P(X<2.5)

=

P(Z<2.13)=

0.9834