Question

According to records in a large hospital, the birth weights of newborns have a symmetric and bell-shaped relative frequency distribution with mean 6.8 pounds and standard deviation 0.5 Approximately what proportion of babies are born with birth weight under 6.3 pounds?

Answer 1

Answer:

15.9% of babies are born with birth weight under 6.3 pounds.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 6.8 pounds

Standard Deviation, σ = 0.5

We are given that the distribution of  birth weights is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(birth weight under 6.3 pounds)

P(x < 6.3)

$P( x < 6.3) = P( z < \displaystyle\frac{6.3 - 6.8}{0.5}) = P(z < -1)$

Calculation the value from standard normal z table, we have,  

$P(x < -1) = 0.159 = 15.9\%$

15.9% of babies are born with birth weight under 6.3 pounds.