Pleaseee helppp me with question 2 !!!
1 answer:
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Answer:
a) 1186
b) Between 1031 and 1493.
c) 160
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with mean of 1262 and a standard deviation of 118.
This means that
a) Determine the 26th percentile for the number of chocolate chips in a bag.
This is X when Z has a p-value of 0.26, so X when Z = -0.643.
(b) Determine the number of chocolate chips in a bag that make up the middle 95% of bags.
Between the 50 - (95/2) = 2.5th percentile and the 50 + (95/2) = 97.5th percentile.
2.5th percentile:
X when Z has a p-value of 0.025, so X when Z = -1.96.
97.5th percentile:
X when Z has a p-value of 0.975, so X when Z = 1.96.
Between 1031 and 1493.
(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip cookies?
Difference between the 75th percentile and the 25th percentile.
25th percentile:
X when Z has a p-value of 0.25, so X when Z = -0.675.
75th percentile:
X when Z has a p-value of 0.75, so X when Z = 0.675.
IQR:
1342 - 1182 = 160
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Let
because that is the range of the inverse cosine funcition.
Also,
![\mathsf{cos\,\theta=cos\!\left[cos^{-1}\!\left(\dfrac{4}{5}\right)\right]}\\\\\\ \mathsf{cos\,\theta=\dfrac{4}{5}}\\\\\\ \mathsf{5\,cos\,\theta=4}](https://tex.z-dn.net/?f=%5Cmathsf%7Bcos%5C%2C%5Ctheta%3Dcos%5C%21%5Cleft%5Bcos%5E%7B-1%7D%5C%21%5Cleft%28%5Cdfrac%7B4%7D%7B5%7D%5Cright%29%5Cright%5D%7D%5C%5C%5C%5C%5C%5C%0A%5Cmathsf%7Bcos%5C%2C%5Ctheta%3D%5Cdfrac%7B4%7D%7B5%7D%7D%5C%5C%5C%5C%5C%5C%20%5Cmathsf%7B5%5C%2Ccos%5C%2C%5Ctheta%3D4%7D)
Square both sides and apply the fundamental trigonometric identity:
But which means 
lies either in the 1st or the 2nd quadrant. So 
is a positive number:
![\mathsf{sin\,\theta=\dfrac{3}{5}}\\\\\\ \therefore~~\mathsf{sin\!\left[cos^{-1}\!\left(\dfrac{4}{5}\right)\right]=\dfrac{3}{5}\qquad\quad\checkmark}](https://tex.z-dn.net/?f=%5Cmathsf%7Bsin%5C%2C%5Ctheta%3D%5Cdfrac%7B3%7D%7B5%7D%7D%5C%5C%5C%5C%5C%5C%0A%5Ctherefore~~%5Cmathsf%7Bsin%5C%21%5Cleft%5Bcos%5E%7B-1%7D%5C%21%5Cleft%28%5Cdfrac%7B4%7D%7B5%7D%5Cright%29%5Cright%5D%3D%5Cdfrac%7B3%7D%7B5%7D%5Cqquad%5Cquad%5Ccheckmark%7D)
I hope this helps. =)
Tags: <em>inverse trigonometric function cosine sine cos sin trig trigonometry</em>
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Let
Also,
Square both sides and apply the fundamental trigonometric identity:
But
I hope this helps. =)
Tags: <em>inverse trigonometric function cosine sine cos sin trig trigonometry</em>