Problem 5CQQ

If boys and girls are equally likely, groups of 400 births have a mean of 200 girls and a standard deviation of 10 girls. Is 185 girls in 400 births an unusually low number of girls?

Answer:

Step 1:

Given that,If boys and girls are equally likely, groups of 400 births have a mean of 200 girls and a standard deviation of 10 girls.

Here , n = 400, = 10.

Using the range rule of thumb to find the minimum usual value μ – 2σ and the maximum usual value μ – 2σ.

minimum: mean - 2(standard deviation)

= 200 - 2(10)

= 180

maximum: mean + 2(standard deviation)

= 200 + 2(10)

= 220

No, because 185 girls is within two standard deviations of the mean.

i.e, 180 < 185 < 220.