A sample of final exam scores is normally distributed with a mean equal to 28 an

Question

A sample of final exam scores is normally distributed with a mean equal to 28 and a variance equal to 25.
1. What percentage of scores are between 23 and 33? (Round your answer to two decimal places.)
2. What raw score is the cutoff for the top 10% of scores? (Round your answer to one decimal place.)
3. What is the proportion below 21? (Round your answer to four decimal places.)
4. What is the probability of a score less than 35? (Round your answer to four decimal places.)

15 0/4 points I Previous Answers Priviterastats2 6.E.017. A sample of final exam scores is normally distributed with a mean equal to 28 and a variance equal to 25. E Part (a) What percentage of scores are between 23 and 33? Round your answer to two decimal places E Part (b) What raw score is the cutoff for the top 10% of scores? (Round your answer to one decimal place.) E Part (c) What is the proportion below 21? (Round your answer to four decimal aCes E Part (d What is the probability of a score less than 35? (Round your answer to four decimal places. You may need to use the appropriate table in Appendix B to answer this question. Compute the z-transformation, then look up the z-scores in the unit normal table. My Notes

Explanation / Answer

here mean =28 and sd=5

1. P(23<x<33)=P(23-28/5<z<33-28/5)=P(-1<z<1)=0.6827

2. P(X>x)=0.10

so z=1.282=x-28/5

hence x=34.41

3. P(x<21)=P(z<-1.4)=0.0808

4.P(x<35)=P(z<1.4)=0.9192

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