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GaryK [48]
3 years ago
9

(1 point) Suppose we will flip a fair coin 100 times. (a) What does 35 heads correspond to on the standard scale? (enter exact a

nswer) (b) What does z=2.4 on the standard scale correspond to on the number of heads scale? (enter exact answer)
Mathematics
1 answer:
vlada-n [284]3 years ago
4 0

Answer:

(a) 35 heads correspond to -3 on the standard scale.

(b) z = 2.4 corresponds to 62 heads on the number of heads scale.

Step-by-step explanation:

(a) If we flip a fair coin once, probability of getting head = 0.5

If we flip a fair coin 100 times, mean number of heads = 100(0.5) = 50

If there are N draws with a P probability of success, the standard deviation (SD) is given as:

SD = \sqrt{(N)(P)(1 - P)}

Here, the probability of getting a head (P) is 0.5 while the number of draws (N) is 100. So,

SD = \sqrt{(100)(0.5)(1-0.5)}

SD = 5

The standard scale value is: (35 - 50) / 5 = -3

Hence, 35 heads correspond to -3 on the standard scale.

(b) The standard scale value is 2.4 and we need to find the number of heads.

(X - 50) / 5 = 2.4

X - 50 = 12

X = 62

Hence, z = 2.4 on the standard scale corresponds to 62 on the number of heads scale.

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Answer:

<h2>C. <em>20,160</em></h2>

Step-by-step explanation:

This question bothers on permutation since we are to select a some people out of a group of people and then arrange in a straight line. If r object are to be arranged in a straight line when selecting them from n pool of objects. This can be done in nPr number of ways.

nPr = n!/(n-r)!

Selection of 6 people out of 8 people can therefore be done in 8C6 number of ways.

8P6 = 8!/(8-6)!

8P6 = 8!/2!

8P6 = 8*7*6*5*4*3*2!/2!

8P6 = 8*7*6*5*4*3

8P6 = 56*360

8P6 = 20,160

<em>Hence this can be done in 20,160 number of ways</em>

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<h2 />

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