the number of chocolate chip cookies is approximately normal

the number of chocolate chip cookies is approximately normally distributed with a mean of 1262 chips and a standard deviation of 117 chips.

(a) determine the 27th percentile for the number of chocolate chips in a bag.

(b) determind the number of chocolate chips in a bag that make up the middle 95% of bags.

Solution

Normal Distribution
Mean ( u ) =1262
Standard Deviation ( sd )=117
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P ( Z < x ) = 0.27
Value of z to the cumulative probability of 0.27 from normal table is -0.613
P( x-u/s.d < x - 1262/117 ) = 0.27
That is, ( x - 1262/117 ) = -0.61
--> x = -0.61 * 117 + 1262 = 1190.279                  
b)
About 95% of the area under the normal curve is within two standard deviations of the mean. i.e.
(u ± 2*s.d)
So to the given normal distribution about 68% of the observations lie in between
=[1262 ± 2 * 117]
= 1028 and 1496