# Solution to BPS Exercise 15.7, 15.15

scores = c(86,63,81,55,72,72,65,66,75,59)

#15.7a
hist(scores)

#15.7b
mu = mean(scores)
print("mean score")
print(mu)

#15.7c
samplescores = sample(scores,4)
print("sample of four, and their mean:")
print(samplescores)
print(mean(samplescores))

#15.7d
n = 10000
trials = replicate(n,mean(sample(scores,4)))
hist(trials)

#15.15b
#You can do this by eye, but here we estimate with the trials:
bigones = length(trials[trials >= 76])
print("proportion of xbar larger than 76:")
print(bigones/n)

#15.15c
print("xbar for students 1,3,5,7:")
print(mean(scores[c(1,3,5,7)]))