Can i ask two more questions relating to statistics?

Question

Consider a binomial distribution with 15 identical trials, and a probability of success of 0.5
a. Find the probability that x = 2 using the binomial tables
b. Use the normal approximation to find the probability that x = 2
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Assume that the population of heights of male college students is approximately normally distributed with mean m of 68 inches and standard deviation s of 3.75 inches. A random sample of 16 heights is obtained.

a. Describe the distribution of x, height of the college student.
b. Find the proportion of male college students whose height is greater than 70 inches.
c. Describe the distribution of , the mean of samples of size 16.
d. Find the mean and standard error of the distribution.
e. Find P ( > 70)
f. Find P ( < 67)

***If there is no answer could I get some hints as to how to solve said problem, thanks.

Answer 1

1)
n=15
p=0.5
q=1-p = 0.5
now find P(2) use table or directly 15 C2 (0.5^2 )(0.5^13)

for normal approximation mean m =np = 15* 0.5 =7.5
std. deviation s.d = sqrt (npq) = 1.936

z =(x-7.5) / 1.936 is standard normal
using correction
P(X=2) = P(1.5
=0.0039 (from tables)


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2)

c) I would guess normal with mean 68 and standard deviation

of 3.75 / sqrt(16) (sample size n = 16)

Also think about student's t distribution if you know only the sample standard deviation

I think e and f are incomplete
anyway you can use the data to standardise and use the tables to find the probability