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leonid [27]
3 years ago
6

A music buff wants to estimate the percentage of students at a midwestern university who believe that elvis is still alive. how

many students should he include in a random sample if he wants a 90% confidence interval that is less than 10 percentage points wide? (choose the sample size that is closest to your solution) question 7 options:
Mathematics
1 answer:
gulaghasi [49]3 years ago
5 0
Since we are not given any information about the proportion, we will assume the sample proportion to be 0.50

so,
p = 0.50
The Error is 10% percentage point. This means that on either side of the population proportion the error is 5% so E = 0.05
z = 1.645 (Z value for 90% confidence interval)

The margin of error for population proportion is calculated as:

E=z* \sqrt{ \frac{p(1-p)}{n} }  \\  \\ 
 \frac{E}{z} = \sqrt{ \frac{p(1-p)}{n} }  \\  \\ 
( \frac{E}{z} )^{2}= \frac{p(1-p)}{n} \\  \\ 
n= p(1-p)* (\frac{z}{E})^{2}  \\  \\ 
n=271

This means 271 students should be included in the sample
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Ten percent of the engines manufactured on an assembly line are defective.
antoniya [11.8K]

Answer:

a) the probability that the first non-defective engine will be found on the second trial is 0.09

b) probability that the third non-defective engine will be found on the fifth trial is 0.00486

c) the Mean is 1.1111  and Variance is 0.1235  

d) the Mean is 3.3333and Variance is 0.3704  

Step-by-step explanation:

Firstly;

Let x be the number of trail on which the rth defective occurs

Also let the probability that an occurrence of a defective be p = 0.10

Here, x follows negative binomial distribution with parameters r and p

The probability mass function of X is as follows:

P(X = x) = [ x -1  p^r ( 1 - p)^(x-r)       ; x = r, r + 1, r + 2, ...

                 r - 1 ]

=   [ x -1  (0.10)^r ( 1 - 0.10)^(x-r)

     r - 1 ]

= [ x -1  (0.10)^r ( 0.9)^(x-r)  ..........n 1..... let this be equatio

    r - 1 ]

This represents the probability that the rth success occurs on the xth trail.  

a)

probability that the first non-defective engine will be found on the second trial?

Substitute r = 1 and x = 2 in equation 1  

P(X = 2)  = [ 2 - 1   (0.10)¹ ( 0.90 )²⁻¹

                   1 - 1 ]

= (0.10) × (0.90)

= 0.09

Therefore, the probability that the first non-defective engine will be found on the second trial is 0.09

b)

probability that the third non-defective engine will be found on the fifth trial?

So we substitute r = 3 and x = 5 in equation 1  

P(X = 5) = [ 5 - 1  (0.10)³ ( 0.90)⁵⁻³

                  3 - 1 ]

=    [ 4    (0.10)³ ( 0.9)²

      2 ]

= 0.00486

Therefore, probability that the third non-defective engine will be found on the fifth trial is 0.00486

Now the formula for the mean of the negative binomial distribution is as follows:  

Mean u = r / p    ------- let this be equation 2

The formula for the variance of the negative binomial distribution also is as follows:  

Variance α² = rq / p²   ---------- let this be equation 3

so

c)

the mean and variance of the number of trials on which the first non-defective engine is found.  

First, let the probability that non-defective engine found be p = 0.90

And q = (1 - p) = 1 - 0.90 = 0.10  

Now we substitute r = 1, p = 0.90 and q = 0.10 in equation 2 & 3simultaneously,

the mean and variances are as follows;

Mean = r/p = 1/0.90 = 1.1111

Variance = rq/p² = (1)(0.10) / (0.90)² = 0.1235  

Therefore the Mean is 1.1111  and Variance is 0.1235  

d)

the mean and variance of the number of trials on which the third non-defective engine is found  

Let the probability that non-defective engine found be p = 0.90

And q = (1 - p) = 1 - 0.90 = 0.10

Now we substitute r = 3, p = 0.90 and q = 0.10 in equation (2) and (3) simultaneously,

the mean and variances are;

Mean = r/p = 3/0.90 = 3.3333

Variance = rq/p² = (3)(0.10) / (0.90)² = 0.3704

Therefore the Mean is 3.3333 and Variance is 0.3704    

5 0
3 years ago
Multiply and simplify if possible.<br> sqrt 5x(sqrt x-5 sqrt 5)
RSB [31]
Making the assumption that your problem looks like this,
\sqrt{5x}(\sqrt{x}-5\sqrt{5})

we use the distributive property to multiply:
\sqrt{5x}\times \sqrt{x}-\sqrt{5x}\times5\sqrt{5}&#10;\\&#10;\\ \sqrt{5x^2} - 5\sqrt{25x}&#10;\\&#10;\\ x\sqrt{5}-25\sqrt{x}
5 0
3 years ago
Simplify.<br><br> 4 x (8 + 5) + 9 can someone help me out plz
Xelga [282]

Step-by-step explanation:

4x(8+5)+9

=52x+9

=52x+9

Description:

The first step is to simplify the equation provided. So in this case the equation is 4 x (8 + 5) + 9.  After that you will get your answer as =52x+9. So in this case 4 x (8 + 5) + 9 = =52x+9.

Answer: =61

Hope this helps.

8 0
2 years ago
Read 2 more answers
The function y = f (x) is graphed below. What is the average rate of change of the function f(x) on the interval - 1 ≤ x ≤ 3?
jonny [76]

Answer:

\displaystyle -2

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

<u>Algebra I</u>

  • Average Rate of Change: \displaystyle \frac{f(b) - f(a)}{b - a}

Step-by-step explanation:

<u>Step 1: Define</u>

Interval -1 ≤ x ≤ 3

a = -1, b = 3

f(a) = f(-1) = 4

f(b) = f(3) = -4

<u>Step 2: Find Average</u>

  1. Substitute in variables [ARC]:                     \displaystyle \frac{f(3) - f(-1)}{3 + 1}
  2. Substitute:                                                   \displaystyle \frac{-4 - 4}{3 + 1}
  3. [Fraction] Subtract/Add:                             \displaystyle \frac{-8}{4}
  4. [Fraction] Divide:                                        \displaystyle -2
4 0
3 years ago
Tell whether the statement is true or false. Tan20 degrees greater than cot20 degrees
Oxana [17]
True because tan(20)=2.1 and cot(20)=is o.44
8 0
3 years ago
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