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IgorLugansk [536]
3 years ago
7

The number of chocolate chips in an​ 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252

1252 and standard deviation 129129 chips. ​(a) what is the probability that a randomly selected bag contains between 11001100 and 14001400 chocolate​ chips? ​(b) what is the probability that a randomly selected bag contains fewer than 10001000 chocolate​ chips? ​(c) what proportion of bags contains more than 12001200 chocolate​ chips? ​(d) what is the percentile rank of a bag that contains 10501050 chocolate​ chips?
Mathematics
1 answer:
svp [43]3 years ago
7 0
The z-score is given by the formula:
z=(x-μ)/σ
μ=1252
σ=129
The answer to the questions given will be as follows:
a] <span>what is the probability that a randomly selected bag contains between 1100 and 1400 chocolate​ chips?
z=(1400-1252)/129
z=1.15625
P(x</span>≤<span>1400)=0.8770

z=(1100-1252)/129
z=0.1190
P(X</span>≤1100<span>)=0.1190

the answer will be:
P(1100</span>≤x≤1400<span>)=0.8770-0.1190=0.758

b]</span><span>what is the probability that a randomly selected bag contains fewer than 1000 chocolate​ chips? 
</span>z=(1000-1252)/129=-1.954
P(X≤1000)=0.0256

c] <span>what proportion of bags contains more than 1200 chocolate​ chips?
z=(1200-1252)/129
z=-0.4031
P(X</span>≥1200<span>)=1-P(X</span>≤1200<span>)=1-0.4031=0.5969

</span>
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