Require answer only for 1(e). Plz use empirical rule approach We flip a coin 100

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Require answer only for 1(e). Plz use empirical rule approach

We flip a coin 100 times (n = 100) and note that it only comes up heads 20% (p = 0.20) of the time.

a. What is the mean () and the standard deviation ()?

b.There is about a 68% chance that the number of heads will be somewhere between ___ and ___.

c. There is about a ____chance that the number of heads will be somewhere between 12 and 28.

d. There is about a ____ chance that the number of heads will be somewhere between eight and 32.

e. Convert the random variable to a standard normal random variable and using the standard normal distribution, find the answers to b), c) and d) again.

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Answer:

Require answer only for 1(e). Plz use empirical rule approach

We flip a coin 100 times (n = 100) and note that it only comes up heads 20% (p = 0.20) of the time.

a. What is the mean () and the standard deviation ()?

b.There is about a 68% chance that the number of heads will be somewhere between ___ and ___.

c. There is about a ____chance that the number of heads will be somewhere between 12 and 28.

d. There is about a ____ chance that the number of heads will be somewhere between eight and 32.

e. Convert the random variable to a standard normal random variable and using the standard normal distribution, find the answers to b), c) and d) again.

Expectation = np = 20

Variance = np(1 - p) = 16

Standard deviation = 4

The empirical rule shows that 68% will fall within the first standard deviation, 95% within the first two standard deviations, and 99.7% will fall within the first three standard deviations of the distribution's average.

a).68% chance that the number of heads will be somewhere between 16 and 24 ( 1 sd limits).

b). Z value for 12, z=(12-20)/4 =-2

Z value for 12, z=(28-20)/4 =2

P( 12<x<28) = P( -2<z<2) =0.95.

c). Z value for 8, z=(8-20)/4 =-3

Z value for 32, z=(32-20)/4 =3

P( 8<x<32) = P( -3<z<3) =0.997.

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