Exercise 1 Albert Einstein, one of the worlds smartest men, reportedly had an IQ

Question

Exercise 1

Albert Einstein, one of the worlds smartest men, reportedly had an IQ of 160.The Stanford Binet IQ scores have a mean of 100 and a standard deviation of 15.

Einstein's IQ converts to the z score of 4.00.

How many standard deviations is Einstein's IQ away from the mean?

Is his IQ considered unusual? Why or Why not?

Exercise 2. (6 points) Female Pulse Rates - Pulse rates of adult females are listed in Data Set 1 "FBODY" in Appendix B. The lowest pulse rate is 56 beats per minute, the mean of the listed pulse rates is 77.5 beats per minute, and their standard deviation is 12.5 beats per minute.

Exercise 3

a. What is the difference between the pulse rate of 56 beats per minute and the mean pulse rate of the females? B. How many standard deviations is that difference found in part (a)? c. Convert the pulse rate of 56 beats per minute to a z score. d. If we consider pulse rates that convert to z scores between -2 and 2 to be neither significantly low nor significantly high, is the pulse rate of 56 beats per minute significant?

Explanation / Answer

Ans:

1)mean=100

standard deviation=15

z=(x-mean)/standard deviation

x=160

z=(160-100)/15=60/15=4

Einstein's IQ is 4 standard deviations away from the mean.

P(z>=4) is approximately 0,so it will consdered unsusal(as probability is <0.05)

(For points having z>3 or z<-3,are considered ouliers)

2)mean=77.5

standard deviation=12.5

a)x=56

x-mean=56-77.5=-21.5

b)z=(56-77.5)/12.5=-1.72

c)it is 1.72 standard deviation away from the mean.

d)As,z=-1.72 lies between z=-2 and +2,so rate of 56 beats is not significantly low .

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