Evaluate the expression.<br> 9.(?)

A film distribution manager calculates that 7% of the films released are flops. If the manager is correct, what is the probabili

diamong [38]

Answer:

0.9909 = 99.09% probability that the proportion of flops in a sample of 404 released films would be greater than 4%

Step-by-step explanation:

I am going to 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:

$p = 0.07, n = 404$ . So

$\mu = E(X) = np = 404*0.07 = 28.28$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{404*0.07*0.93} = 5.13$

If the manager is correct, what is the probability that the proportion of flops in a sample of 404 released films would be greater than 4%?

This is the pvlaue of Z when X = 0.04*404 = 16.16. So

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

$Z = \frac{16.16 - 28.28}{5.13}$

$Z = -2.36$

$Z = -2.36$ has a pvalue of 0.0091

1 - 0.0091 = 0.9909

0.9909 = 99.09% probability that the proportion of flops in a sample of 404 released films would be greater than 4%

7 0

4 years ago

Element X decays radioactively with a half life of 13 minutes. If there are 530 grams of Element X, how long, to the nearest ten

Leona [35]

Answer:

$t \approx 50.4\,min$

Step-by-step explanation:

The time constant of the element X is:

$\tau = \frac{13\,min}{\ln 2}$

$\tau = 18.755\,min$

The decay function has the following form:

$\frac{m}{m_{o}} = e^{-\frac{t}{\tau} }$

$t = -\tau \cdot \ln \frac{m}{m_{o}}$

$t = -(13\,min)\cdot \ln \left(\frac{11\,g}{530\,g} \right)$

$t \approx 50.4\,min$

6 0

3 years ago

How To work this out ?

MrMuchimi

(a) Using the completing the square method, we need to write into the form of where , so
Expand to find the value of c
Notice that we get back the first two terms, the and the .We need to get rid of the last term of '9' as the term was not in the original form. The final form will look like
Hence,
(b)
(c) , square root both sides plus and minus of 2 Hence

6 0

3 years ago

What number must be added to the expression below to complete the square? X^2-7x

Yuki888 [10]

Answer:

49/4

Step-by-step explanation:

x² -7x +(7/2)²=(x-7/2)²

x²-2x·7/2+ (7/2)²=(x²-7/2)²

(7/2)²=49/4

3 0

3 years ago

Please help with question 22

DedPeter [7]

$4.99x + 50 \leqslant 200$

6 0

3 years ago

Evaluate the expression. 9.(?)