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sammy [17]
3 years ago
8

How much difference do a couple of weeks make for birth weight? Late-preterm babies are born with 34 to 36 completed weeks of ge

station. The distribution of birth weights (in grams) for late-preterm babies is approximately N(2750, 560).
1. What is the probability that a randomly chosen late-preterm baby would have a low birth weight (less than 2500 grams)? Round your answer to 4 decimal places.
2. What is the probability that a randomly chosen late-preterm baby would have a very low birth weight (less than 1500 grams)? Round your answer to 4 decimal places.
Mathematics
1 answer:
stiks02 [169]3 years ago
3 0

Answer:

a) 0.3277

b) 0.0128

Step-by-step explanation:

We are given the following information in the question:

N(2750, 560).

Mean, μ = 2750

Standard Deviation, σ = 560

We are given that the distribution of distribution of birth weights is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

a) P (less than 2500 grams)

P(x < 2500)

P( x < 2500) = P( z < \displaystyle\frac{2500 - 2750}{560}) = P(z < -0.4464)

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

P(x < 2500) = P(z < -0.4464) = 0.3277 = 32.77\%

b) P ((less than 1500 grams)

P(x < 1500)

P( x < 1500) = P( z < \displaystyle\frac{1500 - 2750}{560}) = P(z < -2.2321)

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

P(x < 1500) = P(z < -2.2321) = 0.0128 = 1.28\%

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Step-by-step explanation:

a) In its basic form, the ratio would be 750:350. However, to get it to it's most basic form, we must find the greatest common factor (GCF) of 750 and 350, which is 50. Then, we divide both numbers by the GCF so that 750 is 15 and 350 is 7. Therefore, the basic form of the ratio is 15:7.

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