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
marusya05 [52]
2 years ago
14

5. The average age of men at the time of their first marriage is 24.8 years. Suppose the

Mathematics
1 answer:
Paha777 [63]2 years ago
6 0

Answer:

0.0013 = 0.13% probability that the sample mean will be more than 26.

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 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 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 average age of men at the time of their first marriage is 24.8 years. Suppose the standard deviation is 2.8 years.

This means that \mu = 24.8, \sigma = 2.8

Forty-nine married males are selected at random and asked the age at which they were first married.

This means that n = 49, s = \frac{2.8}{\sqrt{49}} = 0.4

Find the probability that the sample mean will be more than 26.

This is 1 subtracted by the pvalue of Z when X = 26. So

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

By the Central Limit Theorem

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

Z = \frac{26 - 24.8}{0.4}

Z = 3

Z = 3 has a pvalue of 0.9987

1 - 0.9987 = 0.0013

0.0013 = 0.13% probability that the sample mean will be more than 26.

You might be interested in
Can someone please explain how to do this​
Nookie1986 [14]

Answer:

the mid point formula for this is x+x/2 and y+y/ 2 so #9would be 1/2, 3/2

7 0
2 years ago
nayeli is a real estate agent. she earns 7.5% commission on each sale she makes. last month she sold two houses. one for $175,00
NNADVOKAT [17]

Answer:

she earned $288.75 in commissions

Step-by-step explanation:

5 0
3 years ago
A crate of pears that usually costs $50 is on sale for 10% off. What is the sale price for the crate of pears?​
lorasvet [3.4K]
Answer:5
Explaining:
10% of 50
= 10%=10/100 = 0.1
= 0.1 (x) times 50
= 5
3 0
2 years ago
Find the side length of the equilateral triangle whose area is the square root of 3 cm2
Alla [95]

Here, Given

Area of Equilateral triangle = 3cm2

therefore, we know;

Area of Equilateral triangle =( \sqrt{3}÷4)×a^{2}

so,

3 =( \sqrt{3}÷4)×a^{2}

3÷( \sqrt{3}÷4) = a^{2}

2.63 cm = a .

The area of ​​an equilateral triangle is the area covered by an equilateral triangle on a two-dimensional plane. An equilateral triangle is a triangle with all sides equal and all angles at 60 degrees. The area of ​​the shape is the number of unit squares that fit inside.

Here, "unit" refers to 1, and a unit square is a square with one side. Alternatively, the area of ​​an equilateral triangle is the total amount of space it surrounds in a two-dimensional plane.

Learn more about Area of  triangle  here: brainly.com/question/17335144

#SPJ4

6 0
2 years ago
Y = -3/4x - 2
oksian1 [2.3K]

Answer:

One Solution

Step-by-step explanation:

Trust me

4 0
3 years ago
Other questions:
  • Day of a measles outbreak at a school, 8 students were identified to have the measles. Each day for the On the first following t
    10·2 answers
  • Alex bought 4 hoodies. Each hoodie cost the same amount and they were on sale for $5 off each. Alex paid a total of $120. How mu
    10·1 answer
  • Suppose one bottle of paint can cover 20 tiles. you have 348 tiles. how many bottles of paint do you need to buy to cover all 34
    7·1 answer
  • Beau can process 36 envelopes for a mailing in 24 minutes. At this rate, how many minutes will it take him to process 120 envelo
    13·1 answer
  • Given the points below, find
    9·1 answer
  • What is the unit rate for 839.68 km in 51.2 h?<br><br> Round to the nearest tenth if necessary
    15·1 answer
  • What dose the point 0,0 represent on the blue line
    6·1 answer
  • Quick math, please help! What is the length of side BC in the triangle? Thank you!
    8·1 answer
  • Which equation in slope-intercept form is equivalent to y+2 = -2(x+4)?
    8·2 answers
  • A passenger train is carrying 403 passengers in 13 cars. How many passenger are in each car?
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!