SOLUTION: The number of chocolate chips in an​ 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips.

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Question 1098855: The number of chocolate chips in an​ 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips.
​(a) What is the probability that a randomly selected bag contains between 1000
and 1500 chocolate​ chips, inclusive?
​(b) What is the probability that a randomly selected bag contains fewer than 1050
chocolate​ chips?
​(c) What proportion of bags contains more than 1175
chocolate​ chips?
​(d) What is the percentile rank of a bag that contains 1450
chocolate​ chips?
I am so confused. Please help me :(

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
The number of chocolate chips in an​ 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips.
​(a) What is the probability that a randomly selected bag contains between 1000
and 1500 chocolate​ chips, inclusive?
​(b) What is the probability that a randomly selected bag contains fewer than 1050
chocolate​ chips?
​(c) What proportion of bags contains more than 1175
chocolate​ chips?
​(d) What is the percentile rank of a bag that contains 1450
chocolate​ chips?
I am so confused. Please help me :(
How are you supposed to do this? Are you supposed to do it manually, or use the TI-83/84 calculator?
Let me START you off/Get you going with a)


MANUALLY
Determine probability of SMALLER VALUE (1,000, in this case)
Using: matrix%281%2C3%2C+Z%2C+%22=%22%2C+%28X+-+mu%29%2Fsigma%29, where:  X = 1,000
                            mu = 1,252
                            sigma = 129

matrix%281%2C3%2C+Z%2C+%22=%22%2C+%28X+-+mu%29%2Fsigma%29 then becomes: 
A Z-score of - 1.95 = .0256


Determine probability of LARGER VALUE (1,500, in this case)
Using: matrix%281%2C3%2C+Z%2C+%22=%22%2C+%28X+-+mu%29%2Fsigma%29, where:  X = 1,500
                            mu = 1,252
                            sigma = 129

matrix%281%2C3%2C+Z%2C+%22=%22%2C+%28X+-+mu%29%2Fsigma%29 then becomes: 
A Z-score of 1.92 = .9726


The probability that a randomly selected bag contains between 1,000 and 1,500 chocolate chips: 

USING THE TI-83/84 CALCULATOR
Select: 2nd VARS → DISTR
CHOICE 2: normalcdf
normalcdf(1000,1500,1252,129)
Press: Enter
You should get: highlight_green%28matrix%281%2C3%2C+.9473466066%2C+or%2C+%2294.7%25%22%29%29, which is the probability that a randomly selected bag contains between 1,000 and 1,500 chocolate chips.