Question

Pregnancy length (in days) is a normally distributed random variable with a mean of 266 days and a standard deviation of 16 days. births that occur before 245 days are considered premature. what is the probability that a randomly selected newborn baby is premature?

Answer 1

The 245 day cutoff has z score (245 - 266) / 16 = -1.3125. The probability that the baby was born prematurely is the probability of having the pregnancy length less than 245 days, or having a z-score less than -1.3125. The probability of having a z-score less than -1.3125 can be looked up on a z-score table: 0.0951

Answer 2

0.095 is the probability that a randomly selected newborn baby is premature.

Explanation:

We are given the following information in the question:

Mean, μ = 266 days

Standard Deviation, σ = 16 days

We are given that the distribution of Pregnancy length is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

a) P(births that occur before 245 days)

P(x < 245)

`P( x < 245) = P( z < \displaystyle(245 - 266)/(16)) = P(z < - 1.3125)`

Calculation the value from standard normal z table, we have,

`P(x < 245) = 0.095 = 9.5\%`

0.095 is the probability that a randomly selected newborn baby is premature.