MATHEMATICS COLLEGE

A stock brokerage has four computers that are used for making trades on the New York Stock Exchange. The probability that a computer fails on any single day is 0.005. Failures occur independently. Any failed computers are repaired after the exchange closes, so each day can be considered an independent trial.(a) What is the probability that all four computers fail on one day?(b) What is the probability that at least one computer fails on a day?(c) What is the mean number of days until a specific computer fails?

Answers

Answer 1
Answer:

Answer:

A) 0 , B)  0.0199 , C) 200

Step-by-step explanation:

Let X denotes no. of computers fail on day

X ~ Bin (n = 4 , p = 0.05)

A] P (X = x) = (n c x) p^x q^n-x

P (X = 4) = (4 c 4) (0.005)^4 (0.995)^0

(0.05)^4 ~ 0

B] P (X > 1) = 1 - P (X < 1) = 1 - P (X = 0)

1 - { ( 4 c 0) (0.005)^0 (0.995)^ 4 }

1 -  (0.995)^ 4 ~ 0.0199

C] Let Y depict mean number of days until a specific computer fails

Y ~ Geom (p = 0.005)

Mean = E (Y) = 1/p = 1/0.05 = 200

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A paint manufacturer made a modification to a paint to speed up its drying time. Independent simple random samples of 11 cans of type A (the original paint) and 9 cans of type B (the modified paint) were selected and applied to similar surfaces. The drying times, in hours, were recorded. The following 98% confidence interval was obtained for μ1 - μ2, the difference between the mean drying time for paint cans of type A and the mean drying time for paint cans of type B: 4.90 hrs < μ1 - μ2 < 17.50 hrs What does the confidence interval suggest about the population means?A. The confidence interval includes 0 which suggests that the two population means might be equal. There​ doesn't appear to be a significant difference between the mean drying time for paint type A and the mean drying time for paint type B. The modification does not seem to be effective in reducing drying times. B. The confidence interval includes only positive values which suggests that the mean drying time for paint type A is greater than the mean drying time for paint type B. The modification seems to be effective in reducing drying times. C. The confidence interval includes only positive values which suggests that the two population means might be equal. There​ doesn't appear to be a significant difference between the mean drying time for paint type A and the mean drying time for paint type B. The modification does not seem to be effective in reducing drying times. D. The confidence interval includes only positive values which suggests that the mean drying time for paint type A is smaller than the mean drying time for paint type B. The modification does not seem to be effective in reducing drying times.
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A hot air balloon descends to the ground. The function h(t) = 210 – 15t can be used to describe the altitude of the balloon as it approaches the ground. Which statement best describes the graph of the function that models the descent of the balloon?A) The graph is discrete because there cannot be fractional values for time.
B) The graph is discrete because there cannot be negative values for altitude.
C) The graph is continuous because there can be fractional values for time.
D) The graph is continuous because there can be negative values for altitude.

Answers

Answer:

Option c

Step-by-step explanation:

Given that a hot air balloon descends to the ground.

The function

h(t) = 210 - 15t

can be used to describe the altitude of the balloon as it approaches the ground.

Here t = time and h = height

Since t cannot be negative we can t starting from 0

t can take any fractional value and h is well defined for any value of t positive

So option c is right
C The graph is continuous because there can be fractional values for time

Compare to the graph f(x)=x^2 the graph of g(x)=(x-2)+3 is the result of translating f(x) 1.2 units up 3 units to the right
2. 2 units down and 3 units up
3. 2 units right and 3 units up
4 2 units left and 3 units right

Answers

Answer:

i believe it is 4 but i'm not so sure

Step-by-step explanation:

:)

Final answer:

The graph of g(x)=(x-2)^2+3 compared to the graph of f(x)=x^2 is translated 2 units to the right and 3 units upwards.

Explanation:

To understand the transformation of graphs in mathematical terms, consider the initial function f(x) = x^2. The transition to the new function g(x)=(x-2)^2+3 is a result of a shift or translation of the graph. This transformation behaves as per the following rule: g(x) = f(x-h)+k where 'h' units is the horizontal displacement and 'k' units is the vertical displacement.

In the function g(x), x shifts two units to the right (as indicated by (x-2)) and three units upward (as indicated by +3).

So, the correct answer is 2 units right and 3 units up.

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your softball team has 8, 10, 9, and 3 hits during four games. Write and solve an equation to find how many hits the team needs in the fifth game to have a total of 40 hits​

Answers

Answer:

10

Step-by-step explanation:

8+10+9+3=30. So, 40-30=10

Answer:10

Step-by-step explanation:

Add 9 to 10 to get 19, then add 3 to get 22, then add 8 to get 30.

A direct mailing company sells computers and computer parts by mail. The company claims that at least 90% of all orders are mailed within 72 hours after they are received. The quality control department at the company often takes samples to check if this claim is valid. A recently taken random sample of 150 orders showed that 129 of them were mailed within 72 hours. Set up the null and alternative hypotheses to test whether the company’s claim is true?

Answers

Answer:

The null and alternative hypothesis are:

H_0: \pi=0.9\n\nH_a:\pi<0.9

There is not enough evidence to support the claim that the company is worng and less than 90% of all orders are mailed within 72 hours after they are received.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The company claims that at least 90% of all orders are mailed within 72 hours after they are received. The company's claim is the null hypothesis, the claim that is going to be tested is if this proportion is significantly less than 90%.

Then, the null and alternative hypothesis are:

H_0: \pi=0.9\n\nH_a:\pi<0.9

The significance level is 0.05.

The sample has a size n=150.

The sample proportion is p=0.86.

p=X/n=129/150=0.86

The standard error of the proportion is:

\sigma_p=\sqrt{(\pi(1-\pi))/(n)}=\sqrt{(0.9*0.1)/(150)}\n\n\n \sigma_p=√(0.0006)=0.024

Then, we can calculate the z-statistic as:

z=(p-\pi+0.5/n)/(\sigma_p)=(0.86-0.9+0.5/150)/(0.024)=(-0.037)/(0.024)=-1.497

This test is a left-tailed test, so the P-value for this test is calculated as:

\text{P-value}=P(z<-1.497)=0.0672

As the P-value (0.0672) is greater than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that less than 90% of all orders are mailed within 72 hours after they are received.

Final answer:

The null hypothesis is that 90% of all orders are shipped within 72 hours, denoted as H0: p = 0.90. The alternative hypothesis is that less than 90% of all orders are shipped within 72 hours, expressed as HA: p < 0.90.

Explanation:

In hypothesis testing, the null hypothesis represents the theory that has been put forward, either because it is believed to be true or because it is used as a basis for argument. In this case, the null hypothesis would be that 90% of all orders are shipped within 72 hours. This can be formulated as H0: p = 0.90 where p represents the proportion of all orders shipped within 72 hours.

The alternative hypothesis on the other hand is the hypothesis used in hypothesis testing that is contrary to the null hypothesis. Here, the alternative hypothesis would be that less than 90% of all orders are shipped within 72 hours. It can be expressed as HA: p < 0.90 where p remains the proportion of orders shipped within 72 hours.

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