Q2

Suppose that diastolic blood pressures (DBPs) for men aged 35-44 are normally distributed with a mean of 80 (mm Hg) and a standard deviation of 10. About what is the probability that a random 35-44 year old has a DBP less than 70?

mean2<- 80
value2<- 70
sd2<- 10
answ2<- pnorm(value2,mean2,sd2)
round(answ2,2)

## [1] 0.16

Q3

Brain volume for adult women is normally distributed with a mean of about 1,100 cc for women with a standard deviation of 75 cc. What brain volume represents the 95th percentile?

mean3<- 1100
sd3<- 75
quantil3<- 0.95
answ3<- qnorm(quantil3,mean3,sd3)
round(answ3,0)

## [1] 1223

Q4

Refer to the previous question. Brain volume for adult women is about 1,100 cc for women with a standard deviation of 75 cc. Consider the sample mean of 100 random adult women from this population. Around what is the 95th percentile of the distribution of that sample mean?

mean4<- 1100
sd4<- 75
n4<- 100
quantile4<- 1.645
var4<- sd4/sqrt(n4)
answ4<- mean4+(var4*quantile4)
answ4

## [1] 1112.338

Q5

You flip a fair coin 5 times, about what’s the probability of getting 4 or 5 heads?

prob4<- choose(5,4)*0.5^4*(1-0.5)^1
prob5<- choose(5,5)*0.5^5*(1-0.5)^0
answ5<- prob4+prob5
round(answ5,2)

## [1] 0.19

Q6

The respiratory disturbance index (RDI), a measure of sleep disturbance, for a specific population has a mean of 15 (sleep events per hour) and a standard deviation of 10. They are not normally distributed. Give your best estimate of the probability that a sample mean RDI of 100 people is between 14 and 16 events per hour?

mean6<- 15
sd6<- 10
n6<- 100
var6a<- 14
var6b<- 16
value61a<- (14-mean6)/(sd6/sqrt(n6))
p14<- pnorm(value61a)
value61b<- (16-mean6)/(sd6/sqrt(n6))
p16<- pnorm(value61b)
answ6<- p16-p14
round(answ6,2)

## [1] 0.68