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
Natali [406]
3 years ago
15

Suppose that 20% of the adult women in the United States dye or highlight their hair. We would like to know the probability that

a SRS of size 200 would come within plus or minus 3 percentage points of this true value. In other words, find probability that pˆ takes a value between 0.17 and 0.23.
Mathematics
1 answer:
Rasek [7]3 years ago
6 0

Answer:

71.08% probability that pˆ takes a value between 0.17 and 0.23.

Step-by-step explanation:

We use the binomial approxiation to the normal 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 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 = 0.2, n = 200. So

\mu = E(X) = np = 200*0.2 = 40

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.2*0.8} = 5.66

In other words, find probability that pˆ takes a value between 0.17 and 0.23.

This probability is the pvalue of Z when X = 200*0.23 = 46 subtracted by the pvalue of Z when X = 200*0.17 = 34. So

X = 46

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

Z = \frac{46 - 40}{5.66}

Z = 1.06

Z = 1.06 has a pvalue of 0.8554

X = 34

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

Z = \frac{34 - 40}{5.66}

Z = -1.06

Z = -1.06 has a pvalue of 0.1446

0.8554 - 0.1446 = 0.7108

71.08% probability that pˆ takes a value between 0.17 and 0.23.

You might be interested in
A number is decreased by seven. Then, the new number is multiplied by 3 to get an answer of -9. What is the original number?
stellarik [79]
4-7= -3
-3x3= -9
answer is C
8 0
3 years ago
Please help i’m having a hard time answering it
pshichka [43]
So we know 5ft to 1cm then
4x5=20ft
6x5=30ft
8 0
3 years ago
Help me please what is i really need help
Scorpion4ik [409]
<h2>Answer: -50.4</h2>

Step-by-step explanation: -6.3 x 8 = -50.4

5 0
3 years ago
HELP ASAP PLS.
Sindrei [870]

Step-by-step explanation:

I have no idea if I'm doing it right but my guess would be to take the values that we get from f(x) and g(x) when x = 1.  Therefore we get that f(x) is equal to 4 and g(x) is equal to -1.  We than just do f/g which is 4/-1 which gives us the final answer of -4 which is option B.

Answer:  Option B, -4

5 0
2 years ago
20 business cards are placed in a hat, 10 belong to women, 10 belong yo men If 2 cards are drawn at once. what's the probability
erik [133]

Answer:

First choice:

               \large\boxed{\large\boxed{5/19}}

Explanation:

<em>The probability that the first is a man's card and the second, a woman's card</em> is calculated as the product of both probabilities, taking into account the fact that the second time the number of cards  in the hat has changed.

In spite of it is said that the cards are drawn at once, since it is stated a specific order for the cards (first is a man's card and the second, a woman's card) you can model the procedure as if the cards were drawn consecutively, instead of at once.

<u>1. Probability that the first is a man's card</u>

  • Number of cards in the hat = 20 (the 20 business card)

  • Number of man's card in the hat: 10

  • Probability = favorable oucomes / possible outcomes = 10/20 = 1/2.

<u />

<u>2. Probability that the second is a woman's card</u>

  • Number of cards in the hat = 19 (there is one less card in the hat)

  • Number of wonan's card in the hat: 10

  • Probability = favorable oucomes / possible outcomes = 10/19.

<u>3. Probability that the first is a man's card and the second, a woman's card</u>

<u />

  • (1/2) × (10/19) = 5/19

That is the first choice.

5 0
2 years ago
Read 2 more answers
Other questions:
  • A large rectangle has side lengths of 8 meters and 6 meters. A smaller rectangle with side lengths of 4 meters and 2 meters is c
    14·1 answer
  • Bradley bought 2 cakes for his class Valentines's party. There are 23 students in his class. How much cake will each student rec
    6·1 answer
  • I don't know exactly what do to do for this type of question
    8·2 answers
  • Using the following to answer the question: p: 3 is an even number q: 9 is an even number Using a truth table, determine whether
    7·1 answer
  • Questions 1-3 40 points
    15·1 answer
  • Heather drove a constant rate
    6·2 answers
  • If AB = 3x - 5 and AC = 5x - 22 , Find AB
    7·1 answer
  • What percentage is 4 dimes?​
    15·1 answer
  • A machine cuts a strip of carpet into two pieces. The length of the smaller piece is 5 meters greater than the length of the lar
    10·1 answer
  • pablo buys 3 servings of jambalaya and 2 drinks for $18 jasmine buys 1 serving and 2 drinks for $9. Write 2 equations based on t
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!