Question

Is that a big baby?

The average birth weight in the US is µ ≈ 120 ounces (7 pounds, 8 ounces) with a standard deviation of σ = 16 ounces (1 pound). Use this information to answer questions 1-4.

A. What is the Z-score for a newborn weighing 112 ounces (7 pounds)?

B. What is the probability that a child will weigh less than 112 ounces (7 pounds) at birth? That is, what is p(X<112)? (Hint: use the Z-score you found for the first question.)

C. So how big is a "big baby"? Let's see how big a newborn must be to be in the top 1% heaviest. First, what is the Z-score you need to use to find the top 1%?

D. How much does that big baby weigh? In other words, what is the value of X such that p(X) < 0.01? (Hint: use the Z-score you found in the last question.) Enter your answer in ounces, not pounds.

Answer 1

Here

µ ≈ 120 ounces

σ = 16 ounces

A) Here X = 112

So

B)

P(X<112)

= P(Z < -0.5)

= 0.3085

C)

Let K be the weight required to be a big baby

So

P(X > K ) = 0.01

But from the standard normal probability table

P(Z > 2.326 ) = 0.01

D)

so

Answer: 157.216 ounces

Note :

• Please round the final answer as per requirement.
• The probability mentioned in the question is wrong.
• Instead of p(X) < 0.01 we should use p(X) > 0.01

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