The number of chocolate chips in an 18ounce bag of chocolate

The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and standard deviation 129 chips. (a) What is the probability that a randomly selected bag contains between 1100 and 1500 chocolate chips? chips? (d) What is the percentile rank of a bag that contains 1450 chocolate chips? Click the icon to view a table of areas under the normal curve. (a) ine probab that a randomly selected bag contams between 11uu and 15UU cnocolate chips is (Round to four decimal places as needed.) (b) The probability that a randomly selected bag contains fewer than 1050 chocolate chips is (Round to four decimal places as needed. (co The proportion of bags that contains more than 1225 chocolate chip s 15 (Round to four decimal places as needed.) Enter your answer in each of the answer boxes.

Solution

a) X= no. of chocolates in a randomly selcted bag
so, P [ 1100 < X < 1500 ] = P [ (1100 - 1252) / 129 < Z < ( 1500-1252)/129 ]
= P [ Z < 1.922481 ] - P [ Z < -1.178295 ] = 0.9727273 -  0.1193396 = 0.8533877..
b) P [ X < 1050 ] = P [ Z < ( 1050-1252) / 129 ] = P [ Z < -1.565891 ] =  0.05868701.....
C) P [ X > 1225 ] = P [ Z > ( 1225-1252) / 129 ] = 1 - P [ Z < -0.2093023 ] = 0.5828939...

d) Z = ( 1450 - 1252 ) / 129....
or, Z = 1.534884....
so, percentile rank = 93.75938