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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?

User Sparko Sol
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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
User Karthik Bammidi
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3 votes

Answer:

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.

User Pkqk
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