1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
svp [43]
3 years ago
9

According to a Yale program on climate change communication survey, 71% of Americans think global warming is happening.† (a) For

a sample of 16 Americans, what is the probability that at least 13 believe global warming is occurring? Use the binomial distribution probability function discussed in Section 5.5 to answer this question. (Round your answer to four decimal places.) (b) For a sample of 160 Americans, what is the probability that at least 110 believe global warming is occurring? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.) (c) As the number of trials in a binomial di
Mathematics
1 answer:
SpyIntel [72]3 years ago
3 0

Answer:

a) 0.2741 = 27.41% probability that at least 13 believe global warming is occurring

b) 0.7611 = 76.11% probability that at least 110 believe global warming is occurring

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

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 samples 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)}.

In this problem, we have that:

p = 0.71

(a) For a sample of 16 Americans, what is the probability that at least 13 believe global warming is occurring?

Here n = 16, we want P(X \geq 13). So

P(X \geq 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 13) = C_{16,13}.(0.71)^{13}.(0.29)^{3} = 0.1591

P(X = 14) = C_{16,14}.(0.71)^{14}.(0.29)^{2} = 0.0835

P(X = 15) = C_{16,15}.(0.71)^{15}.(0.29)^{1} = 0.0273

P(X = 16) = C_{16,16}.(0.71)^{16}.(0.29)^{0} = 0.0042

P(X \geq 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) = 0.1591 + 0.0835 + 0.0273 + 0.0042 = 0.2741

0.2741 = 27.41% probability that at least 13 believe global warming is occurring

(b) For a sample of 160 Americans, what is the probability that at least 110 believe global warming is occurring?

Now n = 160. So

\mu = E(X) = np = 160*0.71 = 113.6

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{160*0.71*0.29} = 5.74

Using continuity correction, this is P(X \geq 110 - 0.5) = P(X \geq 109.5), which is 1 subtracted by the pvalue of Z when X = 109.5. So

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

Z = \frac{109.5 - 113.6}{5.74}

Z = -0.71

Z = -0.71 has a pvalue of 0.2389

1 - 0.2389 = 0.7611

0.7611 = 76.11% probability that at least 110 believe global warming is occurring

You might be interested in
Please help. 5. Give an example of an open equation. (1 point)
Papessa [141]

Answer:

x+4 = 8

(❁´◡`❁)(❁´◡`❁)(❁´◡`❁)

Step-by-step explanation:

An example would be x+4 = 8

(❁´◡`❁)(❁´◡`❁)(❁´◡`❁)

5 0
3 years ago
Read 2 more answers
A salesperson receives step commission on sales calculated as follows:
kykrilka [37]

Answer:

$2278.846

Step-by-step explanation:

Given the following commision steps :

8% on first $1000;

12% next $2000;

20% on sales above $3000

Recorded sales for a week :

Monday $1500.00

Tuesday $3000.00

Wednesday $ 970.00

Thursday $4563.81

Friday $2760.42

This assu es that commision is calculated after weekly sales:

Total:

(1500 + 3000 + 970 + 4563.81 + 2760.42)

= $12794.23

8% on first $1000

0.08 × $1000 = $80

12% of $2000 = $240

20% of $(12794.23 - 3000)

= 0.2 × 9794.23

= 1958.846

Total commision for the week :

$(80 + 240 + 1958.846)

= $2278.846

7 0
3 years ago
DeShawn has $53. He needs at least $76 to buy the jacket he wants. How much more money does he need for the jacket?
Blizzard [7]

Answer:

$23

Step-by-step explanation:

76-53=23

8 0
3 years ago
Read 2 more answers
BRAINLIEST!!!<br> 18. Point p is chosen at random on EH. Find the probability that p is on FG.
shepuryov [24]

Answer:

\frac{2}{5}

Step-by-step explanation:

The total length of this line is 15 units. FG is 6 units long.

This means that the probability of p being on FG would be \frac{6}{15} which can be simplified to \frac{2}{5}

5 0
3 years ago
Read 2 more answers
Isolated triangle 68 perimeter equal sides more than 10 ft use x for the shorter side formula
Ugo [173]

Answer:

Step-by-step explanation:

Find the perimeter of an isosceles triangle whose equal sides have a size of 10 m each and the angle between them equal to 30°. We need to know all sides in order to find the perimeter of this triangle. Let x be the base of this isosceles triangle.

6 0
2 years ago
Other questions:
  • How would you change 125.25% to decimal form?
    11·2 answers
  • #6) Beth saved a total of $30 per month for her first car. Beth saved
    9·1 answer
  • Complete the factorization of 3x2 – 5x + 2.
    5·2 answers
  • Find the absolute value and solve the problem<br> |-23| + |-15|
    10·2 answers
  • 10| x – 4| - 3 &gt; 47​
    12·1 answer
  • What is 0.039 as a fraction?
    15·1 answer
  • Please tell me which ones I should select!!!
    14·1 answer
  • Find the Greatest common factor of 120? Show your work!
    6·1 answer
  • What’s the slope of (-7,2) and (1,4)
    13·1 answer
  • Please help solve this please thank youuuuuu
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!