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
Ivanshal [37]
3 years ago
10

Majesty Video Production Inc. wants the mean length of its advertisements to be 26 seconds. Assume the distribution of ad length

follows the normal distribution with a population standard deviation of 2 seconds. Suppose we select a sample of 21 ads produced by Majesty.a. What can we say about the shape of the distribution of the sample mean time?b. What is the standard error of the mean time? (Round your answer to 2 decimal places)c. What percent of the sample means will be greater than 27.05 seconds?d. What percent of the sample means will be greater than 25.05 seconds?e. What percent of the sample means will be greater than 25.05 but less than 27.05 seconds?"
Mathematics
1 answer:
Paladinen [302]3 years ago
8 0

Answer:

a) By the Central Limit Theorem, approximately normally distributed, with mean 26 and standard error 0.44.

b) s = 0.44

c) 0.84% of the sample means will be greater than 27.05 seconds

d) 98.46% of the sample means will be greater than 25.05 seconds

e) 97.62% of the sample means will be greater than 25.05 but less than 27.05 seconds

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 normally distributed samples are 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.

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(also called standard error) 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.

In this problem, we have that:

\mu = 26, \sigma = 2, n = 21, s = \frac{2}{\sqrt{21}} = 0.44

a. What can we say about the shape of the distribution of the sample mean time?

By the Central Limit Theorem, approximately normally distributed, with mean 26 and standard error 0.44.

b. What is the standard error of the mean time? (Round your answer to 2 decimal places)

s = \frac{2}{\sqrt{21}} = 0.44

c. What percent of the sample means will be greater than 27.05 seconds?

This is 1 subtracted by the pvalue of Z when X = 27.05. So

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

By the Central Limit Theorem

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

Z = \frac{27.05 - 26}{0.44}

Z = 2.39

Z = 2.39 has a pvalue of 0.9916

1 - 0.9916 = 0.0084

0.84% of the sample means will be greater than 27.05 seconds

d. What percent of the sample means will be greater than 25.05 seconds?

This is 1 subtracted by the pvalue of Z when X = 25.05. So

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

Z = \frac{25.05 - 26}{0.44}

Z = -2.16

Z = -2.16 has a pvalue of 0.0154

1 - 0.0154 = 0.9846

98.46% of the sample means will be greater than 25.05 seconds

e. What percent of the sample means will be greater than 25.05 but less than 27.05 seconds?"

This is the pvalue of Z when X = 27.05 subtracted by the pvalue of Z when X = 25.05.

X = 27.05

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

Z = \frac{27.05 - 26}{0.44}

Z = 2.39

Z = 2.39 has a pvalue of 0.9916

X = 25.05

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

Z = \frac{25.05 - 26}{0.44}

Z = -2.16

Z = -2.16 has a pvalue of 0.0154

0.9916 - 0.0154 = 0.9762

97.62% of the sample means will be greater than 25.05 but less than 27.05 seconds

You might be interested in
Convert from Decimal Notation to Scientific Notation
umka21 [38]

Answer:

Hence, 0.026 can be expressed as $2.6 \times 10^{-2}$.

Step-by-step explanation:

- Given 0.026

- Use given, move the decimal point so that first factor is greater than or equal to 1 but less than 10 .

- Then count n and write in scientific notation.

Step 1 of 1

Consider 0.026

$$\Rightarrow 2.6$$

Decimal has moved 2 places to right.

The power will be negative as original no. is less than 1 .

$$\begin{aligned}&2.6 \times 10^{-2} \\&0.026=2.6 \times 10^{-2} .\end{aligned}$$

6 0
2 years ago
A person runs 1/5 miles in 1/40<br> Hour The person's speed is<br> miles per hour.
Minchanka [31]

Answer:

1/5 × 40 = 8

the person's speed is 8 miles per hour

5 0
3 years ago
Can some one explain in an easy way pls
Helga [31]
What needs to be done first is to add up females and males that have passed.

42 + 14 = 56

so out of 56 students who passed 42 females passed 42/56 = 3/4 = 0.75

out of 56 students who passed, 14 males passed which turns into 14/56 = 1/4 = 0.25

check work; 0.75 + 0.25 = 1.00

NOW WE ARE DOING FAILS.

15 + 5 = 20

so out of 20 students who failed, 15 females failed so it turns into 15/20 = 3/4 = 0.75

out of 20 students who failed, 5 males failed. 5/20 = 1/4 = 0.25

check work; 0.75 + 0.25 = 1.00

i hope this helped! :)

7 0
2 years ago
Gina Wilson unit 3: homework 6: Slope intercept form and standard form HELP
Goshia [24]

Answer:

1.) 2x-y=-7 --> y=2x + 7

2.) 5x+3y=12 --> y= -5/3x + 4

3.) x-y=1 --> y= x- 1

4.) x-3y=-15 --> y=1/3x + 5

5.) 8x-10y=20 --> y=4/5x - 2

6.) 14x+6y=36 --> y=-7/3x+6

Step-by-step explanation:

Hope this helped.

8 0
2 years ago
) Sarah donated one-tenth of her salary to an orphanage, one-third of her salary is spent on food, one-fourth of salary on rent
AleksAgata [21]

Answer:

₹ 4000

Step-by-step explanation:

Sarah's salary =₹ 30000

  • one-tenth of her salary to an orphanage= 1/10*₹ 30000= ₹ 3000
  • one-third of her salary is spent on food= 1/3*₹ 30000= ₹ 10000
  • one-fourth of salary on rent and electricity =1/4*₹ 30000= ₹ 7500
  • one-twentieth of her salary on the telephone= 1/12*₹ 30000= ₹ 2500
  • donated some amount to the Prime Minister's relief fund = x
  • She was left with ₹ 3000.

x= ₹ 30000- (₹ 3000+₹ 10000+₹ 7500+₹ 2500+₹ 3000)= ₹ 4000

8 0
3 years ago
Other questions:
  • PHYSICS- I need to rewrite the following numbers in scientific notation in simplest form but am stuck. It also says to include u
    9·2 answers
  • Factor the polynomial.3x^6y^2+81y^2
    15·2 answers
  • 20 pts and a mark!!! A store is having a sale on jelly beans and trail mix. For 6 pounds of jelly beans and 2 pounds of trail mi
    7·1 answer
  • keisha drove 225 miles using 10 gallons of gas. at this rate, how many gallons of gas would she need to drive 441 miles
    12·1 answer
  • What is 55 1/5 - 32 3/4
    8·1 answer
  • Please help me in maths
    5·1 answer
  • Together, two apples have 1/5 gram of fat. How many apples have a total of 4 grams of fat?
    5·1 answer
  • A baseball team has a record of 47 wins and 39 losses. How many games must the team win, in a row, so that the winning percentag
    12·1 answer
  • Celiac disease causes damage to the villi when can cause malnutrition?<br><br> A. True <br> B. False
    5·1 answer
  • On a roadtrip, the distance driven can be represented by the following equation
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!