Question

A population of values has a normal distribution with μ=20.8μ=20.8 and σ=20.5σ=20.5. You intend to draw a random sample of size n=34n=34.
Find P₄₁, which is the score separating the bottom 41% scores from the top 59% scores.
P₄₁ (for single values) =
Find P₄₁, which is the mean separating the bottom 41% means from the top 59% means.
P₄₁ (for sample means) =
Enter your answers as numbers accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

A population of values has a normal distribution with μ=204.5μ=204.5 and σ=84.3σ=84.3. You intend to draw a random sample of size n=53n=53.
Find the probability that a sample of size n=53n=53 is randomly selected with a mean less than 227.7.
P(M < 227.7) =
Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Please show me how you can find this answer in tl84 plus and also write answers so i can understand thanks you

Answer 1

Solution:

Question 1)

Given: A population of values has a normal distribution with μ=20 and σ=20.5.

Sample size = n = 34

Part a) Find P₄₁, which is the score separating the bottom 41% scores from the top 59% scores.
P₄₁ (for single values) =...............?

that is:

P( X < x ) = 0.41

Use following steps in TI 84:

Press 2ND and VARS

Select invNorm(

Enter numbers

Click on Paste and press Enter two times.

Thus we get:

P₄₁ (for single values) = 16.1353

Part b) Find P₄₁, which is the mean separating the bottom 41% means from the top 59% means.
P₄₁ (for sample means) =..............?

We use Standard error instead of standard deviation to find P₄₁ (for sample means).

The standard error is given by:

We use same steps used in part a) in TI 84 plus calculator:

Press 2ND and VARS

Select invNorm(

Enter numbers

Click on Paste and press Enter two times.

thus we get:

Question 2)

Given: A population of values has a normal distribution with μ = 204.5 and σ = 84.3.

Sample size = n = 53

P(M < 227.7) =..............?

Since we have to find probability for sample mean, we use Standard error instead of standard deviation.

The standard error is given by:

Now use following steps in TI 84:

Press 2ND and VARS

Select normalcdf(

We have to find P(M < 227.7) =.....?

Thus lower limit is minus infinity and upper limit is 227.7.

For lower limit , we need to enter minus infinity, so we enter -999999999999 as minus infinity

Press (-) button for - sign.

Thus we get:

Click on Paste and press Enter two times.

Thus we get: