Question

The weight of a newborn babies born on time is normally distributed with a mean of 7.5 pounds in a standard deviation of 1.25 pounds. My nephew weighed 8.5 pounds find the probability of a baby weighs more than he did.

b. The weight of a newborn babies born on time is normally distributed with a mean of 7.5 pounds in a standard deviation of 1.25 pounds find the probability of baby weighs between 6.25 and 8.5 pounds.

Answer 1

(a) 0.2119

(b) 0.6294

Explanation:

μ = 7.5

σ = 1.25

(a)

`Z=(x-\mu)/(\sigma)`

`=(8.5-7.5)/(1.25)`

`=0.8`

P(Z>0.8) = 1 - Ф(0.8)

= 1 - 0.7881

= 0.2119

(b)

`Z1=(x1-\mu)/(\sigma)`

`=(6.25-7.5)/(1.25)`

`=-1`

`Z2=(x2-\mu)/(\sigma)`

`=(8.5-7.5)/(1.25)`

`=0.8`

P(-1<Z<0.8) = Ф(0.8) - Ф(-1)

= 0.7881 - 0.1587

= 0.6294