Question

# In a certain​ country, the mean birth weight for boys 3.23 ​kg, with a standard deviation...

In a certain​ country, the mean birth weight for boys 3.23 ​kg, with a standard deviation of 0.58 kg. Assuming that the distribution of birth weight is approximately​ normal, complete parts a through e below.a. A baby is considered of low birth weight if it weighs less than 2.5 kg.

a. What proportion of baby boys in this country are born with low birth​ weight?

b. What is the​ z-score for a baby boy that weighs 1.5 kg​ (defined as extremely low birth​ weight)?

c. Typically, birth weight is between 2.5 kg and 4.0 kg. Find the probability a baby is born with typical birth weight.

d. matteo weighs 3.4 kg at birth. He fall at what percentile?

e. max's parents are told that their newborn son fall at the 95th . How much does max weigh?

Mean, = 3.23 kg

Standard deviation, = 0.58 kg

Let X(in kg) be the birth weight

(a) The required probability = P(X < 2.5)

= P{Z < (2.5 - 3.23)/0.58}

= P(Z < -1.26) = 0.1038

(b) The corresponding z score = (1.5 - 3.23)/0.58

= -2.983

(c) The required probability = P(2.5 ≤ X ≤ 4)

= P{-1.26 ≤ Z ≤ 1.328)

= 0.8041

(d) Z score corresponding to 3.4 kg is

(3.4 - 3.23)/0.58 = 0.293

Thus, the required percentile = 61.5 th percentile

(e) Corresponding to 95th percentile, the z score = 1.645

Thus, the weight of max = 3.23 + 1.645*0.58

= 4.184 kg