Question

The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3901 grams and a variance of 101.761 if a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be between 3582 and 4443 grams. Round your answer to four decimal places.

Answer 1

Solution:

We are given

µ = 3901

σ^2 = 101761

σ =Sqrt(101761) = 319

We have to find P(3582 < x < 4443)

P(3582 < x < 4443)= P(x<4443 ) - P(x<3582)

Find P(x <4443)

Z = (x - µ)/σ

Z = (4443 - 3901)/319

Z = 1.69906

P(Z<1.69906) = P(x<4443) = 0.955346

(by using z-table)

Now find P(x<3582)

Z = (x - µ)/σ

Z = (3582 - 3901)/319

Z = -1

P(Z<-1) = P(x<3582 ) = 0.158655

(by using z-table)

P(3582 < x < 4443) = P(x<4443 ) - P(x<3582)

P(3582 < x < 4443) = 0.955346 - 0.158655

P(3582 < x < 4443) = 0.796691

Required probability = 0.7967