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Galina-37 [17]
3 years ago
6

The weights of certain machine components are normally distributed with a mean of 5.19 ounces and a standard deviation of 0.05 o

unces. Find the two weights that separate the top 8% and the bottom 8%. These weights could serve as limits used to identify which components should be rejected
Mathematics
1 answer:
Brums [2.3K]3 years ago
4 0

Answer:

The  weight that separate the top 8% by 5.2605 and the weight that separate bottom 8% by 5.1195.

Step-by-step explanation:

We are given that

Mean,\mu=5.19

Standard deviation,\sigma=0.05

We have to find the two weights that separate the top 8% and the bottom 8%.

Let x1 and x2 the two weights that separate the top 8% and the bottom 8%.

Z-value for p-value =0.08 =-1.41

For 8% bottom

Z=\frac{x_1-\mu}{\sigma}=-1.41

\frac{x_1-5.19}{0.05}=-1.41

x_1-5.19=-1.41\times 0.05

x_1=-1.41\times 0.05+5.19

x_1=5.1195

For 8% top

p-Value=1-0.08=0.92

Z- value=1.41

Now,

\frac{x_2-5.19}{0.05}=1.41

x_2-5.19=1.41\times 0.05

x_2=1.41\times 0.05+5.19

x_2=5.2605

(x1,x2)=(5.1195,5.2605)

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Answer:

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Step-by-step explanation:

For each consumer, there are only two possible outcomes. Either they recognize the name, or they do not. The probability of a customer recognizing the name is independent of anu other customer. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

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The brand name of Mrs. Fields (cookies) has a 90% recognition rate.

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Sample of 10

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