Respuesta :
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:
0.095 is the probability that a randomly selected newborn baby is premature.
Step-by-step 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:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
a) P(births that occur before 245 days)
P(x < 245)
[tex]P( x < 245) = P( z < \displaystyle\frac{245 - 266}{16}) = P(z < - 1.3125)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x < 245) = 0.095 = 9.5\%[/tex]
0.095 is the probability that a randomly selected newborn baby is premature.
