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
ryzh [129]
3 years ago
15

The mean life of a television set is 119119 months with a standard deviation of 1414 months. If a sample of 7474 televisions is

randomly selected, what is the probability that the sample mean would differ from the true mean by less than 1.11.1 months? Round your answer to four decimal places.
Mathematics
1 answer:
Pepsi [2]3 years ago
3 0

Answer:

0.5034 = 50.34% probability that the sample mean would differ from the true mean by less than 1.1 months

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 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.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, the sample means with size n of at least 30 can be approximated to a normal distribution with mean

In this problem, we have that:

\mu = 119, \sigma = 14, n = 74, s = \frac{14}{\sqrt{74}} = 1.6275

What is the probability that the sample mean would differ from the true mean by less than 1.11 months?

This is the pvalue of Z when X = 119 + 1.1 = 120.1 subtracted by the pvalue of Z when X = 119 - 1.1 = 117.9. So

X = 120.1

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

By the Central Limit Theorem

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

Z = \frac{120.1 - 119}{1.6275}

Z = 0.68

Z = 0.68 has a pvalue of 0.7517

X = 117.9

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

Z = \frac{117.9 - 119}{1.6275}

Z = -0.68

Z = -0.68 has a pvalue of 0.2483

0.7517 - 0.2483 = 0.5034

0.5034 = 50.34% probability that the sample mean would differ from the true mean by less than 1.1 months

You might be interested in
How do you solve the factoring of 3t^3-7t^2-3t+7
Serjik [45]

Step-by-step explanation:

<h3>t^2(3t-7) -1(3t-7)</h3>

(3t-7) (t^2-1)this is the answer

7 0
2 years ago
Write the number in 2 equivalent forms as a fraction, decimal, or percent.
hjlf

Answer:

96% percent and fraction is 24/25

8 0
3 years ago
Read 2 more answers
The midpoint of stack A B with bar on top has coordinates of (4, -9). Endpoint A has coordinates (-3, -5). What are the coordina
Radda [10]
I think it's B with the bar on top
3 0
3 years ago
(4x^2+3x −5)+(x^2 −7x+10)
olga nikolaevna [1]

Answer:

5x^{2}  -4x +5

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Grant takes an Uber from his hotel to a restaurant. The cost of the Uber is a $2.95 initial charge plus $2.25 per mile. Which eq
Papessa [141]
The answer is Y= 2.25x+2.95
6 0
2 years ago
Other questions:
  • A drive way is 40 yards long. About how many meters lobg is it
    11·2 answers
  • the size of a rectangular computer monitor is determined by the length of its diagonal. If a computer monitor has a length of 24
    13·2 answers
  • #1 What is the value of the expression 7–3? Answers: A. –21 B. - 1/343 C.1/343 D. 343  #2What is the value of the expression 1/5
    12·2 answers
  • Which of the following algebraic expressions can be used to express the statement "one less than x squared?"
    7·2 answers
  • What is the value of the expression when n = 3? 12 24 42 54
    7·2 answers
  • 11. How is the graph of g(x) = 5x² - 2<br> related to the graph of f(x)= x2?
    11·1 answer
  • What is the meaning of y from y=kx?
    15·1 answer
  • How do movement skills in volleyball transfer to tennis?​
    13·1 answer
  • Find the volume of a rectangular prism that is 10 cm long, 3 cm wide, and 2 cm high. Please draw and label the prism​
    10·1 answer
  • Write a real-world problem to compare fractions.then solve the problem
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!