Question

please show all work for problems

1. What % of the curve is below Z of -1.5 2. what % of the curve is below 2 of 2.85 3. What of the curve is above 2 of .07 4. What ? of the curve is above 2 of -.17 5. What f of the curve is between Z of 2.85 and .07 6. Percentile Rank of 35 is z of 7. Percentile Rank of 76 is z of 8. On an I.Q. test for MAT 102 students given in Dust Bowl Iowa, 1947, it was found that the = 110 and the 5. What % of the I.Q. scores were above 120? 9. Using the same data as in 8, what % of the scores were between 120 and 902 10. In a distribution of 100 scores, 4 = 60 and 6 = 10, what is less than 75? 11. What is the percentile rank of score 47.5? 12. What score is exceeded by 60% of the students? 13. Find a range of scores centered at the mean that includes 50% of the score. 14. There are 10 scores less than what score? 15. The 95th grade from the bottom has a percentile rank of

Answer 1

Here we need to find the probabilites corresponding to the given Z scores.

1)

here we need to determine % of curve below Z score of -1.5

i.e.,

$\small P(Z < -1.5) = \phi(-1.5) = 0.0668072$

where $\small \phi(.)$ is the CDF of standard normal distribtution which we have calculated in R

code is :

> pnorm(-1.5)

[1] 0.0668072

2)

Here we need to determine % of curve below Z score of 2.85

i.e.,

$\small P(Z < 2.85) = \phi(2.85) = 0.997814$

R code :

> pnorm(2.85)

[1] 0.997814

3)

Here we need to determine the % of curve above 0.07

i.e.,

$\small P(Z >0.07)=1-P(Z \leq 0.07) = 1-\phi(0.07) = 1-0.5279032 = 0.4720968$

R code:

> pnorm(0.07)

[1] 0.5279032

4)

Here we need to determine the % of curve above -0.17

i.e.,

Plz > -0.17) = 1 - P(Z < -0.17) = 1 - 0(-0.17) = 1 -0.4325051 = 0.5674949

R code:

> pnorm(-0.17)

[1] 0.4325051

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