The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with a mean of 266 days and a standard deviation of 16 days. between what two values do the middle 95% of the lengths of all pregnancies fall?
a. between 218 and 314 days
b. between 234 and 298 days
c. between 202 and 330 days
d. between 250 and 282 days

[ 250 , 282 ]

Step-by-step explanation:

A Normal Distribution N ( 0,1)

We know one of the characteristics of a normal distribution is the symmetry and the fact that in the interval of

μ₀ - σ   and  μ₀ + σ   are found the 95.5 % of all values

In our case we have μ₀ = 266   and the standard deviation  σ = 16

So    μ₀ - σ     ⇒  266 - 16  = 250  the lowest value for the interval and

       μ₀ + σ     ⇒  266 + 16 = 282  the highest value for the interval

The interval  with 95.5 % of all values is

[ 250 , 282 ]

a² + b²= c²

24² + 7² = c²

c= 25

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