Binomial Distribution

Question

The distribution of weights for the population of females in the United States is approximately normal with mean µ = 135.4 pounds and standard deviation σ = 21.3 pounds. 

1. What is the probability that among six females selected at random from the population, at least two will have a weight outside the range 125 to 160 pounds?

I got 0.8826 but I just wanted to double-check my answer

Answer 1

Let's see if we have the right idea:

You calculate z_hi , z_lo (z = (x - μ)/σ ) and use the normal distribution to find the area between the z values: A (-inf to z_hi) - A(-inf to z_lo). I get .563. Probability of any one outside of limits is 1-P = .437

2 or more out of 6 with a weight outside is the same as 5 or 6 out of 6 inside the range.

Bernoulli Dist:

₆C₀ (.563)⁶ + ₆C₁(.563)⁵(.437)

( The first term is all 6 inside, 2nd is 5 inside and 1 out which happens in 6 ways.)

Good luck. You may have misunderstood the question as this probability should be < .5