a recipe for cookies calls for 2/3 of a cup of sugar per batch. elena used 6 2/3 cups of sugar to make multiple bathes did she m
2 answers:
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Answer:
0.2755
Step-by-step explanation:
We intend to make use of the normal approximation to the binomial distribution.
First we'll check to see if that approximation is applicable.
For p=10% and sample size n = 500, we have ...
pn = 0.10(500) = 50
This value is greater than 5, so the approximation is valid.
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The mean of the distribution we'll use as a model is ...
µ = p·n = 0.10(500)
µ = 50
The standard deviation for our model is ...
σ = √((1-p)µ) = √(0.9·50) = √45
σ ≈ 6.708204
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A continuity correction can be applied to better approximate the binomial distribution. We want p(t ≤ 9.1%) = p(t ≤ 45.5). For our lookup, we will add 0.5 to this limit, and find p(t ≤ 46).
The attached calculator shows the probability of fewer than 45.5 t's in the sample is about 0.2755.
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Answer:
n = 8
Step-by-step explanation:
"By inspection" is an appropriate method.
We are asked to compare the expressions
n·n
8·n
and find the value(s) of n that makes them equal. <em>By inspection</em>, we see that n=8 will make these expressions equal. We also know that both expressions will be zero when n=0.
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More formally, we could write ...
n^2 = 8n . . . . the two formulas give the same value
n^2 -8n = 0 . . . . rearrange to standard form
n(n -8) = 0 . . . . . factor
Using the zero product rule, we know the solutions will be the values of n that make the factors zero. Those values are ...
n = 0 . . . . . makes the factor n = 0
n = 8 . . . . . makes the factor (n-8) = 0
Generally, we're not interested in "trivial" solutions (n=0), so the only value of n that is of interest is n = 8.
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A lot of times, I find a graphing calculator to be a quick and easy way to find function argument values that make expressions equal.
