Question

Consider a normal distribution curve where the middle 35 % of the area under the curve...

Consider a normal distribution curve where the middle 35 % of the area under the curve lies above the interval ( 3 , 11 ). Use this information to find the mean, μ and the standard deviation, σ of the distribution.

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Solution:

P(3<X<11) = 0.35

P(X<3) = (1 - 0.35)/2 = 0.325

Z = (X - mean)/SD

-0.45376 = (3 - mean)/SD

(by using z-table)

-0.45376*SD = (3 - mean)

Mean - 0.45376*SD = 3

(equation 1)

Now, we have

P(X>11) = (1 - 0.35)/2 = 0.325

Z = (X - mean)/SD

0.45376 = (11 - mean)/SD

0.45376*SD = (11 - mean)

Mean + 0.45376*SD = 11

(equation 2)

Now, solve equation 1 and 2 for the values of mean and SD.

By adding equation 1 and 2, we get

Mean - 0.45376*SD = 3

Mean + 0.45376*SD = 11

===========================

2*Mean = 14

Mean = 14/2 = 7

Mean = 7

Mean - 0.45376*SD = 3

7 - 0.45376*SD = 3

0.45376*SD = 7 - 3 = 4

SD = 4/0.45376 = 8.815233

SD = 8.815233

μ = 7

σ = 8.82

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
(1 point) Consider a normal distribution curve where the middle 45 % of the area under...
(1 point) Consider a normal distribution curve where the middle 45 % of the area under the curve lies above the interval ( 5 , 20 ). Use this information to find the mean, μμ , and the standard deviation, σσ , of the distribution
(1 point) Consider a normal distribution curve where 90-th percentile is at 11 and the 25-th...
(1 point) Consider a normal distribution curve where 90-th percentile is at 11 and the 25-th percentile is at 9. Use this information to find the mean,  ?μ , and the standard deviation, ?σ , of the distribution. a) ?=μ=   b) ?=σ=   (1 point) Length of skateboards in a skateshop are normally distributed with a mean of 31.3 in and a standard deviation of 0.5 in. The figure below shows the distribution of the length of skateboards in a skateshop. Calculate...
Consider a normal distribution curve where 65-th percentile is at 19 and the 30-th percentile is...
Consider a normal distribution curve where 65-th percentile is at 19 and the 30-th percentile is at 10. Use this information to find the mean, μ , and the standard deviation, σ , of the distribution. a) μ= b) σ=
Consider a normal distribution curve where 90-th percentile is at 17 and the 40-th percentile is...
Consider a normal distribution curve where 90-th percentile is at 17 and the 40-th percentile is at 8. Use this information to find the mean, μ , and the standard deviation, σ , of the distribution. a) μ= b) σ=
(1 point) Consider a normal distribution curve where 90-th percentile is at 11 and the 25-th...
(1 point) Consider a normal distribution curve where 90-th percentile is at 11 and the 25-th percentile is at 9. Use this information to find the mean, μ , and the standard deviation, σ , of the distribution. a) ?= 9.6873 (right answer) b) σ = 1.025 (not correct?) I have tried this answer but webwork will not accept it. Is there possibly another answer
Consider a normal distribution curve where 80-th percentile is at 19 and the 20-th percentile is...
Consider a normal distribution curve where 80-th percentile is at 19 and the 20-th percentile is at 1. Use this information to find the mean, ? μ , and the standard deviation, ? σ , of the distribution.  Note: this is a tricky problem, you should get out a pen and paper and work through it carefully.
1. the area under the normal distribution curve that lies within one standard deviation of the...
1. the area under the normal distribution curve that lies within one standard deviation of the mean is approxiamtely ____%. 2. for a normal distribution curve with a mean of 10 and a standard deviation of 5, what is the range of the variable thay defines the area under the curve correaponding to a probability of approximately 68%? true or false: 3. a probability can be greater than one, but not equal to zero. 4. quartiles are used in box...
Find the area to the left of x = 28 under a normal distribution curve with...
Find the area to the left of x = 28 under a normal distribution curve with μ = 35 and σ = 5 . Round your answer to four decimal places.
1. About ____ % of the area under the curve of the standard normal distribution is...
1. About ____ % of the area under the curve of the standard normal distribution is between z = − 1.863 z = - 1.863 and z = 1.863 z = 1.863 (or within 1.863 standard deviations of the mean). 2. About ____ % of the area under the curve of the standard normal distribution is outside the interval z=[−2.24,2.24]z=[-2.24,2.24] (or beyond 2.24 standard deviations of the mean). 3. About ____ % of the area under the curve of the...
(a)Find the area under the standard normal curve that lies outside the interval between =z−1.73 and...
(a)Find the area under the standard normal curve that lies outside the interval between =z−1.73 and =z1.99. (b)Find the area under the standard normal curve that lies outside the interval between =z−1.75 and =z0.99. (c)Find the area under the standard normal curve that lies outside the interval between =z0.89 and =z1.41. (d)Find the area under the standard normal curve that lies outside the interval between =z−1.80 and =z−1.33.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT