If 1 1/2 sections are 3/4 mile long, how long is each section?

For a particular diamond mine, 81% of the diamonds fail to qualify as "gemstone grade". A random sample of 92 diamonds is analyz

Fed [463]

Answer:

68.79% probability that more than 79% of the sample diamonds fail to qualify as gemstone grade

Step-by-step explanation:

We use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

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

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 pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 92, p = 0.81$

So

$\mu = E(X) = np = 92*0.81 = 74.52$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{92*0.81*0.19} = 3.76$

Find the probability that more than 79% of the sample diamonds fail to qualify as gemstone grade.

This is 1 subtracted by the pvalue of Z when X = 0.79*92 = 72.68. So

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

$Z = \frac{72.68 - 74.52}{3.76}$

$Z = -0.49$

$Z = -0.49$ has a pvalue of 0.3121

1 - 0.3121 = 0.6879

68.79% probability that more than 79% of the sample diamonds fail to qualify as gemstone grade

4 0

3 years ago

Two number cubes are rolled for two separate events:

MatroZZZ [7]

Let us first make the sample space for the event A. The Sample Space will be:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5)

(5,1) (5,2) (5,3) (5,4)

(6,1) (6,2) (6,3)

As can be clearly seen the Sample Space for the event A has 30 elements in it.

Now, it is given in the question that the event A has already occurred and we need to find the probability of the event B occurring <u><em>given that the event A has already occurred.</em></u>

Now, as we can see, from the sample space, only 11 events out of the 30 are the events of interest to us. This is shown in bold below:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5)

(5,1) (5,2) (5,3) (5,4)

(6,1) (6,2) (6,3)

Thus, the probability that the event B occurs given that the event A has already occurred is:

$P(B|A)=\frac{11}{30}\approx0.367$

In percentage the required probability is 36.7% approximately.

3 0

3 years ago

I need helppppppp.....

RoseWind [281]

Answer:

6/7

Step-by-step explanation:

-3 - 4 -7 -7

---------- = -------- = ------

5 - (-1) 5 + 1 6

Do the inverse of -7/6: 6/7

4 0

3 years ago

Find the potential solution to the equation log4(2 – x) = log4(–5x – 18).

NNADVOKAT [17]

Log₄(2 – x) = log₄(–5x – 18).

Since the logs have the same basis (4) & are equal then:

(2 – x) = (–5x – 18). . Now solve for x & you will find x = -5

4 0

3 years ago

Read 2 more answers

Can anyone answer this?

defon

Answer:

Ayo its Jose is the only one who was trying to get me to do the thank you usa for the support of the joy luck club the story is about a mother that lost every thing in China and whent to America to start a new life but she make her daughter do something that she don't want to be ninja in and she is not sending her

6 0

1 year ago