#21-24 need help with

Mathematics

1 answer:

fredd [130]3 years ago

4 0

Answer:

117

Step-by-step explanation:

1×2^6 + 1×2^5 + 1×2^4 + 0×2^3 + 1×2^2 + 0×2^1 + 1×2^0

1×64+1×32+1×16+0×8+1×4+0×2+1×1

=64+32+16+0+4+0+1

=117

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Halloween Candy Halloween is Kelly's favorite holiday of the year! Based on experience, Kelly knows that on average, each house

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Using the <u>normal distribution and the central limit theorem</u>, it is found that there is an approximately 0% probability that the total number of candies Kelly will receive this year is smaller than last year.

Normal Probability Distribution

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

It 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, which is the percentile of X.
By the Central Limit Theorem, for n instances of a normal variable, the mean is $n\mu$ while the standard deviation is $s = \sigma\sqrt{n}$ .

In this problem:

Mean of 4 candies, hence $\mu = 4$ .
Standard deviation of 1.5 candies, hence $\sigma = 1.5$ .
She visited 35 houses, hence $n = 35, \mu = 35(4) = 140, s = 1.5\sqrt{4} = 3$