Question

The average weight of a newborn baby is 6.4 pounds with standard deviation 1.2 pounds.  If a baby girl weigh is in the 90th percentile how much does she weigh?

multiple choice:

a) 6.4

b) 12.8

c) 7.9

Answer 1

We assume that the weight is normally distributed.

Let X be the r.v denoting the weight of a new born baby.

Given $P(X<X_0)=0.9$

Now $\mu=6.4 \;\&\; \sigma =1.2$

Thus,

X- Define Z:= such that Z ~ N(u = 0,02 = 1)

.

X- XO - P(X<XO) = P ,) = P(Z <20) = 0.9

Now, So from Normal Distribution table we we get $Z_0=1.285$

$\frac{X_0 -\mu}{\sigma }=1.285$

$\frac{X_0 -6.4}{1.2 }=1.285$

$X_0 =1.285(1.2)+6.4=7.936\approx 7.9$

So option C is correct