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Question 11 options: the lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. what is the probability that a pregnancy lasts at least 300 days?

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Think of (or draw) a standard normal curve with mean 268 days and std dev 15 days.

Calculate the z-score for 300 days:

       300-268          32
z = -------------- = --------- = 2.13
           15                15

Now find the area under the curve to the right of z = + 2.13.  Alternatively, find the area under the curve to the left of this z and subtract the result from 1.00.

I used my TI-83's DISTR function normalcdf( to calculate the area to the right of 300 days:

normalcdf(300,infinity, 268, 15) = 0.016, or about 0.02.

Only about 2% of pregnancies will last 300 days or longer.

The probability that a pregnancy lasts at least 300 days with a mean of 268 days and a standard deviation of 15 days is 0.0164 or 1.646%.

What is normally distributed data?

Normally distributed data is the distribution of probability which is symmetric about the mean.

  • The mean of the data is the average value of the given data.
  • The standard deviation of the data is the half of the difference of the highest value and mean of the data set.

The lengths of human pregnancies are normally distributed, with a mean of 268 days and a standard deviation of 15 days.

[tex]\mu=268\\\sigma=15[/tex]

The probability that a pregnancy lasts at least 300 days has to be find out. Thus, the score is,

[tex]x=300[/tex]

For this, calculate the z score,

[tex]z=\dfrac{x-\mu}{\sigma}\\z=\dfrac{300-268}{15}\\z=2.1333[/tex]

The commutative probability for the z score 2.1333 is 0.0164 or 1.646%.

Thus, the probability that a pregnancy lasts at least 300 days with a mean of 268 days and a standard deviation of 15 days is 0.0164 or 1.646%.

Learn more about the normally distributed data here;

https://brainly.com/question/6587992

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