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?
pnorm(70, mean=80, sd=10)## [1] 0.1586553Brain 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?
qnorm(.95, mean=1100, sd=75)## [1] 1223.364Refer 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. What is the 95th percentile of the distribution of that sample mean?
sd <- 75 / sqrt(100)
qnorm(.95, mean=1100, sd=sd)## [1] 1112.336You flip a fair coin 5 times, about what’s the probability of getting 4 or 5 heads?
1 - pbinom(3, 5, .5)## [1] 0.1875The 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?
sd <- 10 / sqrt(100)
pnorm(16, mean=15, sd) - pnorm(14, mean=15, sd)## [1] 0.6826895The number of people showing up at a bus stop is assumed to be Poisson with a mean of 5 people per hour. You watch the bus stop for 3 hours. About what’s the probability of viewing 10 or fewer people?
ppois(10, 3*5)## [1] 0.1184644