15 A teacher gives a test and gets normally distributed results with a mean of 5

Question

15 A teacher gives a test and gets normally distributed results with a mean of 50 and a standard deviation of 10.  The letter grade A is assigned only to those in the top 10%.  What score will a student need to receive an A?

(a) > 62.8 (b) > 66.8 (c) > 68.8 (d) > 52.5   

16 Refer to question 15 above.  What percentage of students will have a score between 37 and 76?

(a) .4032 (b) .4953 (c) .8985 (d) .9357

17 Refer to question 15 above.  What percentage of students will have a score of 69 or higher?

(a) .4713 (b) .9713 (c) .0287 (d) .5287

18 The standard normal distribution is a normal probability distribution that has a mean of 1 and a standard deviation of 0.

(a) True (b) False

8. The scores on a Statistics exam are normally distributed with a mean 75 with a standard deviation of 5. If nine students are randomly selected what is the probability that their mean score is greater than 68.

(a) .0808 (b) -.4000 (c) .9192 (d) .0001 (e) .9999

29. Refer to question 28. Suppose that students with the lowest 10% of scores are placed on academic probation, what is the cutoff score to avoid being placed on academic probation?

(a) > 81.4 (b) > 68.6 (c) -.28 (d) -1.28 (e) .8997

Explanation / Answer

1)

Z value for top 10 % can be found from normal tables as 1.281551

or 1.281551 = (x-50)/10 or x = 62.81

Hence,answer is A.

2) For second question , we have to fing the probabilty between z= (37-50)/10 = -1.3 and z = (76-50)/10 = 2.6

THis is equal to Cumulative probability for z <2.6 minus the cumulative probabilty for z= -1.3 which is 0.995339-0.0968 =0.8995

3) 69 is 1.9 standard deviations away from the mean. This can be found out from table as 0.028717

18- False, Standard normal distribution has mean of 0 and standard deviation of 1

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