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goldenfox [79]
3 years ago
10

A university considers giving only pass/fail grades to freshmen to reduce competition and stress. The student newspaper intervie

ws faculty members and reports their opinions of the proposed policy. Suppose that 70% of the faculty favor the pass/fail proposal. Assuming 50 faculty members are interviewed. The goal is to find the probability that a majority (26 or more) will favor the proposal.
Mathematics
1 answer:
astra-53 [7]3 years ago
8 0

Answer:

0.9983 = 99.83% probability that a majority will favor the proposal.

Step-by-step explanation:

We use the normal approximation to the binomial 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 distributions 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)}.

Suppose that 70% of the faculty favor the pass/fail proposal. Assuming 50 faculty members are interviewed.

This means, respectively, that p = 0.7, n = 50

Mean and standard deviation:

\mu = E(X) = np = 50*0.7 = 35

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{50*0.7*0.3} = 3.24

Probability that a majority (26 or more) will favor the proposal.

Using continuity correction, this is P(X \geq 26 - 0.5) = P(X \geq 25.5), which is 1 subtracted by the pvalue of Z when X = 25.5. So

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

Z = \frac{25.5 - 35}{3.24}

Z = -2.93

Z = -2.93 has a pvalue of 0.0017

1 - 0.0017 = 0.9983

0.9983 = 99.83% probability that a majority will favor the proposal.

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Damm [24]

Answer:

The perfect squares are the squares of the whole numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100....

Step-by-step explanation:

the square root of 1 is 1 b/c 1^2=1 (and so on)

8 0
3 years ago
The Lupu Bridge in China is 12,795 ft long. The Hart Bridge in the USA is 3,845 ft long. About how much longer is the Lupu Bridg
AleksAgata [21]
You subtract the length of the Lupu Bridge by the length of thee Hart Bridge after you round them to the nearest thousandth and you get your final answer!
 12,795 -> 13,000
   3,845 -> 4,000
 13,000 - 4,000 = your answer
4 0
2 years ago
A salesperson earns 7.5% commission on each vehicle sold. What price
Eddi Din [679]
Hey there! I’m just going to write out how I would solve this.

3,000=7.5%⋅x
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3,000⋅13 1/3=x
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5 0
2 years ago
Does anyone know how to do this help please
statuscvo [17]

Answer:

\boxed{\begin{array}{c|c|c|c|c|c|c|c} \bf x &\rm -3 &\rm -2 &\rm -1 &\rm 0 &\rm 1 &\rm 2 &\rm 3 \\\\ \bf y & \rm 0 &\rm -4 &\rm -6&\rm -6 &\rm -4&\rm 2 &\rm 6 \end{array}}

Step-by-step explanation:

A quadratic function is given to us . And we need to fill out the table by using the function . The given function is ,

\rm\implies y = x^2+x - 6

Here we need to substitute the different values of x , to get the different values of y.

<u>Put</u><u> </u><u>x </u><u>=</u><u> </u><u>-</u><u>3</u><u> </u><u>:</u><u>-</u><u> </u>

\rm\implies y = 3^2-3-6\\

\rm\implies y = 9 - 3 - 6 \\

\rm\implies y = 0

<u>Put </u><u>x </u><u>=</u><u> </u><u>-</u><u>2</u><u> </u><u>:</u><u>-</u><u> </u>

\rm\implies y = 2^2-2-6\\

\rm\implies y = 4 -2-6\\

\rm\implies y = -4

<u>Put</u><u> </u><u>x </u><u>=</u><u> </u><u>-</u><u>1</u><u> </u><u>:</u><u>-</u><u> </u>

\rm\implies y = -1^2-1-6\\

\rm\implies y = 1 -1-6 \\

\rm\implies y = -6

<u>Put </u><u>x </u><u>=</u><u> </u><u>1</u><u> </u><u>:</u><u>-</u><u> </u>

\rm\implies y = 1^2+1-6\\

\rm\implies y = 2 -6

\rm\implies y = -4

<u>Put </u><u>x </u><u>=</u><u> </u><u>2</u><u> </u><u>:</u><u>-</u><u> </u>

\rm\implies y = 2^2+2-6\\

\rm\implies y = 4 +2-6\\

\rm\implies y = 2

<u>Put </u><u>x </u><u>=</u><u> </u><u>3 </u><u>:</u><u>-</u><u> </u>

\rm\implies y = 3^2+3-6\\

\rm\implies y = 9 +3-6\\

\rm\implies y = 6

<u>Final </u><u>table</u><u> </u><u>:</u><u>-</u><u> </u>

\boxed{\begin{array}{c|c|c|c|c|c|c|c} \bf x &\rm -3 &\rm -2 &\rm -1 &\rm 0 &\rm 1 &\rm 2 &\rm 3 \\\\ \bf y & \rm 0 &\rm -4 &\rm -6&\rm -6 &\rm -4&\rm 2 &\rm 6 \end{array}}

7 0
3 years ago
6+(-4)= please help me I don’t here it :)
kirill115 [55]

Answer:

2

Step-by-step explanation:

6 0
2 years ago
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