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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?

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.

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