91影视

Low birth weights are recognized as weights lesser than 5.5lb or 2495g.

The birth weights follow Normal distribution with a mean of 3152.0g and a standard deviation of 693.4g.

a.

Let X be the random variable for birth weight which follows a normal distribution

$$\begin{gathered} X~N\left(渭,{蟽}^2\right) \\ ~鈥�N\left(3152,{693.4}^2\right) \end{gathered}$$

The probability of birth weight lesser than 2495g can be expressed as follows:

$P\left(X<2495\right)$

The z score associated with the birth weights 2495 computed as:

$$\begin{gathered} z=鈥�\frac{x-渭}{蟽} \\ =鈥�\frac{2495-3152.0}{693.4} \\ =鈥�-0.95 \end{gathered}$$

The probability that weight is less than 2496gis expressed as:

$P\left(X<2495\right)=鈥�P\left(Z<-0.95\right)鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�鈥�...1)$

From the standard normal table, the cumulative probability of z = -0.95 is obtained from the cell intersection of row value -0.9 and column value 0.05, which is 0.1711.

Thus,

$P\left(X<2496\right)=0.1711$

Thus, the probability of weight lesser than 2495 g is 0.1711.

b.

Significantly low weights are all those birth weights that have the probability of lesser than 0.05 to appear.

That is,

$P\left(X<x\right)猢�0.05$, where x is the maximum weight below which the weights are significantly low.

The probability of birth weight having a probability of 0.05 or less can be expressed as:

$$\begin{gathered} P\left(X<x\right)=P\left(Z<z\right) \\ =鈥�0.05 \end{gathered}$$

From the standard normal table, the area of 0.05 is observed corresponding to the row value -1.6 and column value between 0.04 and 0.05, which implies the z score is -1.645.

Substitute the value of z as follows:

$$\begin{gathered} z=鈥�\frac{x-渭}{蟽} \\ x=鈥�渭+蟽脳z \\ =鈥�3152-1.645脳693.4 \\ =2011.357 \end{gathered}$$

Therefore, all birth weights lesser than 2011.4 g are considered to be significantly low.

c.

The birth weights are significantly low if they are 2011.35 g or less, which have only a 5% chance to appear in the selection.

Also, birth weights lower than 2496 g are considered low birth rates with 17.11% chances to appear.

Thus, any weight that lies between 2011.5 g and 2496 g is recognized as low birth weight but actually is not significantly low (rare).