Question

Assume that the weight of two year old babies have distribution that is approximately normal with a mean of 29 pounds and a standard deviation of 3 pounds. what weight of two year old baby corresponds to 10th percentile?

Answer 1

Answer:

25.15 ponds is the weight of two year old baby corresponds to 10th percentile.      

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 29 pounds

Standard Deviation, σ = 3 pounds

We are given that the distribution of weight of two year old babies is a bell shaped distribution that is a normal distribution.

Formula:

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

We have to find the value of x such that the probability is 0.10

P(X < x)  

$P( X < x) = P( z < \displaystyle\frac{x - 29}{3})=0.10$  

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

$P(z < -1.282) = 0.10$

$\displaystyle\dfrac{x - 29}{3} = -1.282\\x = 25.154 \approx 25.15$

Thus, 25.15 ponds is the weight of two year old baby corresponds to 10th percentile.