The lengths of pregnancies are normally distributed with a mean of 269 days and

Question

The lengths of pregnancies are normally distributed with a mean of 269 days and a standard deviation of 15 days. Find the probability of a pregnancy lasting 309 days or longer. If the length of pregnancy is in the lowest 4%, then the baby is premature. Find the length that separates premature babies from those who are not premature. The probability that a pregnancy will last 309 days or longer is. (Round to four decimal places as needed.) Babies who are born on or before days are considered premature. (Round to the nearest integer as needed.)

Explanation / Answer

a)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    309      
u = mean =    269      
          
s = standard deviation =    15      
          
Thus,          
          
z = (x - u) / s =    2.67      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2.67   ) =    0.0038 [ANSWER]

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b)

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.04      
          
Then, using table or technology,          
          
z =    -1.75      
          
As x = u + z * s,          
          
where          
          
u = mean =    269      
z = the critical z score =    -1.75      
s = standard deviation =    15      
          
Then          
          
x = critical value =    242.75   = 243 days [ANSWER]  

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