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3 years ago

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200 students in a high school senior class are surveyed about what majors they intend to declare in college. Of the 200 students

, 80 plan to major in mathematics, 100 plan to major in computer science, and 30 plan to pursue a double major in mathematics and computer science. Using this information, answer each of the following questions. Let M be the event that a randomly selected student plans to major in mathematics and C be the event that a randomly selected student plans to major in computer science. What is P(M), left parenthesis, M, right parenthesis, the probability that a student plans to major in mathematics?

1 answer:

dedylja [7]3 years ago

5 0

Answer:

<u><em>P(M) = 0.4</em></u>

Explanation:

<u>1. Build a two-way frequency table:</u>

To have a complete understanding of the scenary build a two-way frequency table.

<u>Column and rows:</u>

Major in math No major in math Total

Major in CS

No major in CS

Total

<u>200 students:</u>

Major in math No major in math Total

Major in CS

No major in CS

Total 200

<u>80 plan to major in mathematics:</u>

Major in math No major in math Total

Major in CS

No major in CS

Total 80 200

<u>100 plan to major in computer science</u>:

Major in math No major in math Total

Major in CS 100

No major in CS

Total 80 200

<u>30 plan to pursue a double major in mathematics and computer science</u>:

Major in math No major in math Total

Major in CS 30 100

No major in CS

Total 80 200

<u>Complete the missing numbers by subtraction</u>:

Major in math No major in math Total

Major in CS 30 70 100

No major in CS 100

Total 80 120 200

Major in math No major in math Total

Major in CS 30 70 100

No major in CS 50 50 100

Total 80 120 200

<u>2. What is P(M), the probability that a student plans to major in mathematics?</u>

P(M) = number of students who plan to major in mathematics / number of students

P(M) = 80 / 200 = 0.4

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damaskus [11]

Answer:

$\textsf{C)}\quad g(x)=\dfrac{1}{2}(x-8)^2-8$

Vertex = (8, -8)

Step-by-step explanation:

<u>Standard form</u>: $y=ax^2+bx+c$

<u>Vertex form</u>: $y=a(x-h)^2+k$

where (h, k) is the vertex

<u>Intercept form</u>: $y=a(x-p)(x-q)$

where p and q are the x-intercepts

Therefore, the form that most quickly reveals the vertex is

$g(x)=\dfrac{1}{2}(x-8)^2-8$

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An engineer wishes to determine the width of a particular electronic component. If she knows that the standard deviation is 3.3

anyanavicka [17]

Answer:

n=465 rounded up to the nearest integer

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

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$\sigma=3.3$ represent the population standard deviation

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n represent the sample size (variable of interest)

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =0.3 mm and we are interested in order to find the value of n, if we solve n from equation (4) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025,0,1)", and we got $z_{\alpha/2}=1.960$ , replacing into formula (b) we got:

$n=(\frac{1.960(3.3)}{0.3})^2 =464.8336 \approx 465$

So the answer for this case would be n=465 rounded up to the nearest integer

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