Question

(a) In a sample of 360 student GPAs, the mean is 3.20 with a standard deviation of 0.22.
        Use the Empirical rule to find how many GPAs fall in the interval [3.20, 3.64]
       (b) True or False: Probabilities ALWAYS lie in the interval [ 0 , 1].
       (c) Explain your choice in (b) above.

Answer 1

Answer)

According to the emperical rule

If the data is normally distributed

Then 68% lies in between mean - s.d and mean + s.d

95% lies in between mean - 2*s.d and mean + 2*s.d

99.7% lies in between mean - 3*s.d and mean + 3*s.d

Mean = 3.2

S.d = 0.22

3.2 = mean

3.64 = mean + (2*s.d)

As the normal distribution is symmetrical about mean

So, 95/2 = 47.5% lies in between 3.2 and 3.64

Expected value is given by n*p

N = 360

P = 0.475

N*p = 171

B)

Yes probability always lies in between [0, 1]

True

C)

Probability is given by favorable/total

For example we have a sample size of 100

And we need to know what is the probability that some one likes icecream

If after surveying 60 told they like icecream

Probability = 60/100 = 0.6

If 0 told they like icecream then 0/100 = 0

If 100 told they like icecream then 100/100 = 1

So, probability cannot be less than 0 or greater than 1