Assume the gestation period approximates a normal curve with

Assume the gestation period approximates a normal curve with a mean of 270 days and a standard deviation of 15 days. What proportion of gestation periods will be:

Between 240 days and 260 days?

Greater than 290 days?

Solution

a)

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    240      
x2 = upper bound =    260      
u = mean =    270      
          
s = standard deviation =    15      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -2      
z2 = upper z score = (x2 - u) / s =    -0.666666667      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.022750132      
P(z < z2) =    0.252492538      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.229742406   [answer]

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b)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    290      
u = mean =    270      
          
s = standard deviation =    15      
          
Thus,          
          
z = (x - u) / s =    1.333333333      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.333333333   ) =    0.09121122 [answer]