Question

1. Based on U.S. Bureau of Justice data, 16% of persons arrested are women. If 400 arrest cases are randomly selected, estimate the probability that more than 60 women were arrested. Since this is discrete data, use the binomial distribution.

I got the answer 0.628 and it is not correct.

2. The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. If we stipulate that a baby is premature if the length of pregnancy is in the lowest 3%, find the number of days that separates premature babies from those who are not premature.

Here I got the answer 296 days and it is not correct.

Thank you

Answer 1

Solution :

Given that,

1) p = 0.16

q = 1 - p = 1 - 0.16 = 0.84

n = 400

Using binomial distribution,

= n * p = 400 * 0.16 = 64

= n * p * q = 400 * 0.16 * 0.84 = 7.33

P(x > 60) = 1 - P(x < 60)

= 1 - P((x - ) / < (60 - 64) / 7.33)

= 1 - P(z < -0.55)

= 1 - 0.2912

= 0.7088

2) mean = = 268

standard deviation = = 15

Using standard normal table,

P(Z < z) = 3%

= P(Z < z ) = 0.03

= P(Z < -1.88 ) = 0.03  

z = -1.88

Using z-score formula,

x = z * +

x = -1.88 * 15 + 268

x = 239.8

x = 240 days