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dusya [7]
3 years ago
12

Jeff is baking a cake. The recipe says that he has to mix 32 grams of vanilla powder to the flour. Jeff knows that 1 cup of that

particular vanilla floor has a mass of 128 grams. He added 2/3 of a cup of vanilla powder to the flower. Should Jeff add more vanilla powder to make the exact recipe, or did he go over and by what amount?
Mathematics
1 answer:
Lady bird [3.3K]3 years ago
8 0
The situation above described that Jeff added two - thirds of 128 to the flour. The numerical value of (2/3)(128) is 85.33 grams. The recipe says to add only 32 grams of vanilla flour.

Hence, Jeff went over the prescribed amount.

To determine the excess amount, subtract 32 from 85.33 which has a numerical value of 53.33 grams.
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Answer:

b) 0.2961

c) 0.2251

d) Mean = 11.25, Standard deviation =  1.667  

Step-by-step explanation:

We are given the following information:

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a) Conditions for binomial probability distribution

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Then the number of trucks undergoing a brake inspection follows a binomial distribution, where

P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}

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b) P(proportion of groups will between 8 and 10 trucks pass the inspection)

We have to evaluate:

P(8\leq x \leq 10) = P(x = 8) + P(x = 9) + P(x = 10)\\= \binom{15}{8}(0.75)^8(1-0.75)^7 + \binom{15}{9}(0.75)^9(1-0.75)^6 + \binom{15}{10}(0.75)^{10}(1-0.75)^5\\= 0.0393 + 0.0917 + 0.1651\\= 0.2961

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P(x = 3)\\= \binom{15}{3}(0.25)^3(1-0.25)^{12}\\=0.2251

d) Mean and standard deviation

\mu = np = 15(0.75) = 11.25\\\sigma = \sqrt{np(1-p)} = \sqrt{15(0.75)(1-0.75)} = 1.667

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