Suppose that the distribution of IQ's of North Catalina State University's students can be approximated by a normal model with mean 130 and standard deviation 8 points. Also suppose that the distribution of IQ's of Chapel Mountain University's students can be approximated by a normal model with mean 120 and standard deviation 10 points. Question 1. You select a student at random from each school. Determine the probability that the North Catalina State University student's IQ is at least 5 points higher than the Chapel Mountain University student's IQ.

Question

07-11-2019
Mathematics

contestada

Suppose that the distribution of IQ's of North Catalina State University's students can be approximated by a normal model with mean 130 and standard deviation 8 points. Also suppose that the distribution of IQ's of Chapel Mountain University's students can be approximated by a normal model with mean 120 and standard deviation 10 points. Question 1. You select a student at random from each school. Determine the probability that the North Catalina State University student's IQ is at least 5 points higher than the Chapel Mountain University student's IQ.

Respuesta :

Otras preguntas

Question Answer O A True O B False Question Answer O A True O B False Question Answer OA O B True False Using logarithmic differentiation we obtain that the der

Kamirah and her family of 7 people are ordering pizza for dinner. In the table below, you can see how much pizza each person is planning on eating. Use the info

After 100 years, we want to use game theory and apply it to our current situation when the world is dealing with Covid-19 and the problem of Vaccination and how

What would be the effect of connecting a voltmeter in series with components of a series electrical circuit? [2] 1.2 What would be the effect of connecting an a

A market supply curve has three prices $7.50, $8.00 and $8.50 with a quantity supplied of 6 tonnes at the price of $7,50, 10 tonnes at $8.00, and 14 tonnes at $

5. A firm must decide between two designs A and B. Their effective income rate is 50%. If the desired after-tax return on investment is 8% per year, which alter

is 6km is not as far as 6 miles true or false

Would the biacromial measure be a better assessment for a predictor of CG in women or males? a. Women b. Men

A population of size 200 has a mean of 112 and a standard deviation of 40. If X is the mean of a random sample of size 50, i. find the mean of the sampling dist

Common allocation bases are a. direct labor dollars, direct hours, direct material dollars b. direct labour dollars, direct labor dollars, machine hours c. dire

FelisFelis FelisFelis · Answer 1 · 2019-11-07T15:18:59+01:00

Answer:

The required probability is 0.6517

Step-by-step explanation:

Consider the provided information.

North Catalina State University's students can be approximated by a normal model with mean 130 and standard deviation 8 points.

μ₁ = 130 and σ₁ = 8

Chapel Mountain University's students can be approximated by a normal model with mean 120 and standard deviation 10 points.

μ₂ = 120 and σ₂ = 10

As both schools have IQ scores which is normally distributed, distribution of this difference will also be normal with a mean of μ₁-μ₂ and standard deviation will be [tex]\sqrt{\sigma_1^2+\sigma_2^2}[/tex]

Therefore,

μ = 130-120=10

[tex]\sigma = \sqrt{8^2+10^2}=12.806[/tex]

Now determine the probability of North Catalina State University student's IQ is at least 5 points higher than the Chapel Mountain University student's IQ:

[tex]z=\frac{\bar x-\mu}{\sigma}[/tex]

[tex]z=\frac{5-10}{12.806}\approx-0.39[/tex]

Now by using the z table we find the z- score of -0.39 is 0.6517.

Hence, the required probability is 0.6517