Question

Suppose medical records indicate that the length of newborn babies(in inches) is normally distributed with a mean of 20 and a standard deviation of 2.6 find the probability that a given infant is between 14.8 and 25.2 inches long

Answer 1

Answer: 95

Step-by-step explanation:

Hope this helps!

Answer 2

Answer:

P=0.954 or 95.4%

Step-by-step explanation:

Using the formula for the standardized normal distribution to find Z:

$Z=\frac{X-\mu}{\sigma}$

Where μ is the mean (μ=20) and σ is the standard deviation (σ=2.6).  

$Z_{1} =\frac{14.8-20}{2.6}=-2.0$

$Z_{1} =\frac{25.2-20}{2.6}=2.0$

In the table of the normal distribution, we can look for positive values z, and these values are going to represent the area under the curve between z=0 and the values searched. the negatives values are found by symmetry (with the corresponding positive value but remember this area is under the left side of the curve).  To find a value in the table, find the units in the first column and the follow over the same row till you find the decimals required.

$P_1=0.4772$

$P_2=0.4772$

$P_1$ represents the probability of length being between 14.8 and 20 (the mean) and $P_2$ represents the probability of length being between 20 and 25.2, The requested probability is the sum of these two.

$P=P_1+P_2=0.954$