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Mnenie [13.5K]
2 years ago
9

Suppose that 90% of all dialysis patients will survive for at least 5 years. In a simple random sample of 100 new dialysis patie

nts, what is the probability that the proportion surviving for at least five years will exceed 80%, rounded to 5 decimal places
Mathematics
1 answer:
Keith_Richards [23]2 years ago
5 0

Answer:

The  probability   P(\^ p  >  0.80) =  0.99957

Step-by-step explanation:

From the question we are told that

     The population proportion is  p  =  0.90

     The sample size is  n  =  30

  Generally mean of the sampling distribution is  \mu_{\= x } =  p =  0.90

Generally the standard deviation is mathematically represented as

      \sigma  = \sqrt{\frac{p( -p )}{n} }

=>    \sigma  = \sqrt{\frac{0.90( 1 -0.90 )}{100} }

=>    \sigma  = 0.03

Generally the he probability that the proportion surviving for at least five years will exceed 80%, rounded to 5 decimal places is mathematically represented as

       P(\^ p  >  0.80) =  P(\frac{ \^ p - p }{ \sigma }  >  \frac{0.80 - 0.90}{0.03} )

Generally \frac{\^p - p}{\sigma}  =  Z(The standardized \  value  \  of  \^  p)

So  

    P(\^ p  >  0.80) =  P(Z  >  -3.33 )

From the z-table P(Z  >  -3.33 ) = 0.99957

So

    P(\^ p  >  0.80) =  0.99957

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11. The sales tax rate is 6.9%
Norma-Jean [14]

Answer:

40.1%

Step-by-step explanation:

I am assuming that 192 is in 100%.

100% = 192

I then represent the value that we are looking for with x.

x% = 77

By dividing both equations (100% = 192 and x% = 77) and remembering that both left hand sides of BOTH equations have the percentage unit (%).

\frac{100}{x} = \frac{77}{192}

Now, of course, we take the reciprocal, or inverse, of both sides:

\frac{x}{100} = \frac{7}{192}

x = 40.1%

Thus making the answer: 40.1% of 192 is 77.

7 0
2 years ago
Point E belongs to diagonal AC of parallelogram ABCD (labeled counterclockwise) so that AE:EC=2:1. Line BE intersects CD at poin
Svetach [21]

Consider two triangles AEB and CEF. In these triangles:

  1. ∠AEB≅∠CEF (as vertical angles);
  2. ∠EAB≅∠ECF (lines AB and CD are parallel and AC is transversal, then these angles are congruent as alternate interior angles);
  3. ∠ABE≅∠CFE (lines AB and CD are parallel, BF is transversal, then these angles congruent as alternate interior angles).

Thus, by AAA theorem, \triangle AEB\sim \triangle CEF.

Corresponding sides of similar triangles are proportional, then

\dfrac{AB}{CF}=\dfrac{AE}{EC},\\ \\\dfrac{AB}{CF}=\dfrac{2}{1},\\ \\AB=2CF.

ABCD is a parallelogram, then AB=CD.

Therefore,

CD=2CF and CD=DF+CF. Equate these two expressions:

DF+CF=2CF,

DF=CF.

This gives you that DF:CF=1:1.

Answer: 1:1


7 0
2 years ago
For two events A and B, a student calculates that P(A and B) = 0.46 and P(B|A) = 0.31. Explain how you can tell that the student
ololo11 [35]
Conditional probability formula is:P ( A and B ) = P ( A ) · P ( B / A )0.46 = P ( A ) · 0.31P ( A ) = 0.46 : 0.31P ( A ) = 1.48And this is impossible because 0 ≤ P ( A ) ≤ 1The student obviously made a mistake.

3 0
2 years ago
Solve 4x - 5 = 7 + 4y for y
Mandarinka [93]

Answer:

<h2>y = x - 3</h2>

Step-by-step explanation:

4x - 5 = 7 + 4y           <em>subtract 7 from both sides</em>

4x - 5 - 7 = 7 - 7 + 4y

4x - 12 = 4y            <em>divide both sides by 4</em>

4x/4 - 12/4 = 4y/4

x - 3 = y

3 0
2 years ago
On the last day of vacation, the Ramirez family drove 252 miles from a state park to its home. The drive covered 35% of the tota
kirill115 [55]

Answer:

Step-by-step explanation:

35 percent of total miles traveled (say T)is 252 miles.

(35/100) * T=252

T=(252*100)/35 => T=720 miles

So total distance the Ramirez family traveled during its vacation is 720 miles

4 0
2 years ago
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