### Bell-shaped curve for sampling distribution of sample

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Q1) How does bell-shaped curve for sampling distribution of sample means for samples of size n =120 compare to bell-shaped curve for sampling distribution of sample means for samples of size n =95?

Q2) Let a binomial distribution with 14 identical trials, and probability of success of 0.4

i) Determine probability that x =3 using binomial tables.

ii) Utilize normal approximation to determine the probability that x=3.

Q3) Find out whether each of distributions given below represents probability distribution. Justify your answer

a)  x 1 2 3 4

P(x) 1/4 5/12 1/3 1/6

b)  x 3 6 8
P(x) 0.1 3/5 0.3

c)  x 20 30 40 50
P(x) 0.2 -0.2 0.7 0.3

Q4) Four cards are chosen, one at a time from a standard deck of 52 cards. Let x represents number of aces drawn in set of 4 cards.

a) If this experiment is completed with no replacement, describe why x is not a binomial random variable.

b) If this experiment is completed with replacement, describe why x is a binomial variable.

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