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
torisob [31]
3 years ago
15

A corporation is considering a new issue of convertible bonds, mandagemnt belives that the offer terns will be founf attractiv b

y 20% of all its current stockholders, suppoer that the belif is correct, a random sample of 130 stockholderss is taken.
a. What is the standard error of the sample proportion who find this offer attractive?
b. What is the probability that the sample proportion is more than 0.15?
c. What is the probability that the sample proportion is between 0.18 and 0.22?
d. Suppose that a sample of 500 current stockholders had been taken. Without doing the calculations, state whether the probabilities in parts (b) and (c) would have been higher, lower, or the same as those found.

Mathematics
2 answers:
ella [17]3 years ago
4 0

Answer:

a. What is the standard error of the sample proportion who find this offer attractive? =  0.0351

b. What is the probability that the sample proportion is more than 0.15? = 0.9222

c. What is the probability that the sample proportion is between 0.18 and 0.22? =  0.4314

Step-by-step explanation:

see attachment for explanation

dezoksy [38]3 years ago
4 0

Answer:

Step-by-step explanation:

Given that,

p = 0.20

1 - p = 1 - 0.20 = 0.80

n = 130

\mu\hat p = p = 0.20

A) \sigma \hat p =  \sqrt[p( 1 - p ) / n] = \sqrt [(0.20 * 0.80 ) / 130] = 0.0351

B) P( \hat p > 0.15) = 1 - P( \hat p < 0.15)

= 1 - P(( \hat p - \mu \hat p ) / \sigma \hat p < (0.15 - 0.20) / 0.0351 )

= 1 - P(z < -1.42)

Using z table

= 1 - 0.0778

= 0.9222

C) P(0.18 < \hat p < 0.22)

= P[(0.18 - 0.20) / 0.0351 < ( \hat p - \mu \hat p ) / \sigma \hat p < (0.22 - 0.20) / 0.0351]

= P(-0.57 < z < 0.57)

= P(z < 0.57) - P(z < -0.57)

Using z table,    

= 0.7157 - 0.2843

= 0.4314

You might be interested in
Common Core Sheets
kiruha [24]
144/145

Convert any mixed numbers to fractions
Then your initial equation becomes
48/5 divided by 29/3
5 0
2 years ago
Read 2 more answers
What is 5x(12.28) +30/2
scoundrel [369]

Answer:

its 61.4x+15

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
The mean of a population is 74 and the standard deviation is 15. The shape of the population is unknown. Determine the probabili
Lena [83]

Answer:

a) 0.0548 = 5.48% probability of a random sample of size 36 yielding a sample mean of 78 or more.

b) 0.9858 = 98.58% probability of a random sample of size 150 yielding a sample mean of between 71 and 77.

c) 0.5793 = 57.93% probability of a random sample of size 219 yielding a sample mean of less than 74.2

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean of a population is 74 and the standard deviation is 15.

This means that \mu = 74, \sigma = 15

Question a:

Sample of 36 means that n = 36, s = \frac{15}{\sqrt{36}} = 2.5

This probability is 1 subtracted by the pvalue of Z when X = 78. So

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

By the Central Limit Theorem

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

Z = \frac{78 - 74}{2.5}

Z = 1.6

Z = 1.6 has a pvalue of 0.9452

1 - 0.9452 = 0.0548

0.0548 = 5.48% probability of a random sample of size 36 yielding a sample mean of 78 or more.

Question b:

Sample of 150 means that n = 150, s = \frac{15}{\sqrt{150}} = 1.2247

This probability is the pvalue of Z when X = 77 subtracted by the pvalue of Z when X = 71. So

X = 77

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

Z = \frac{77 - 74}{1.2274}

Z = 2.45

Z = 2.45 has a pvalue of 0.9929

X = 71

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

Z = \frac{71 - 74}{1.2274}

Z = -2.45

Z = -2.45 has a pvalue of 0.0071

0.9929 - 0.0071 = 0.9858

0.9858 = 98.58% probability of a random sample of size 150 yielding a sample mean of between 71 and 77.

c. A random sample of size 219 yielding a sample mean of less than 74.2

Sample size of 219 means that n = 219, s = \frac{15}{\sqrt{219}} = 1.0136

This probability is the pvalue of Z when X = 74.2. So

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

Z = \frac{74.2 - 74}{1.0136}

Z = 0.2

Z = 0.2 has a pvalue of 0.5793

0.5793 = 57.93% probability of a random sample of size 219 yielding a sample mean of less than 74.2

5 0
3 years ago
Kelly has nine pieces of ribbon. She recorded the length of each piece in the line plot shown.
Ugo [173]

Answer: 44 inches

Step-by-step explanation:

The 3 longest are 14.5 14.5 and 15 so the answer is adding them and 44 is the answer.

6 0
3 years ago
Will mark brainlist if right
dlinn [17]

Answer: C.

Step-by-step explanation:

7 0
2 years ago
Other questions:
  • Which of the following shows 27/54 written in Prime factored form to help in reducing the fraction to simplest form?
    11·1 answer
  • In a 2-card hand, what is the probability of holding only face cards?
    14·1 answer
  • Calculate the number in the middle of 14.5 and 5.2
    15·2 answers
  • 18.50x2.6 what is the answer helppppp!!!!!!!!!!!!!!
    15·2 answers
  • An equilateral triangle is folded in half. What type of triangle is formed?
    11·1 answer
  • Illustrate the distributive property to solve 144/8
    14·1 answer
  • (−4x <br> 4<br> +6x <br> 2<br> +3)−(5x <br> 2<br> −3)
    7·1 answer
  • What's the common factor of 3 8 2 and 5
    6·1 answer
  • A person walking across a bridge accidentally drops an orange into the river below from a height of 40 feet. The function h = −1
    15·2 answers
  • 4(x + 2)- 6 = 14
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!