The scores on a university examination are normally distributed with a mean of 62 and a standard deviation of 11. If the bottom 5% of the students will fail the course, what is the lowest mark that a student can have and still be awarded a passing grade?
Roll one 6-sided die 8 times. The probability of getting exactly 3 ones in those 8 rolls is given by:
The number of telephone calls that pass through a switchboard has a Poisson distribution with mean equal to 2 per minute. The probability that no telephone calls pass through the switchboard in two consecutive minutes (2 minutes and then 2 minutes) is:
In a large population of university students, 70% of the students own an iPhone. If you take a random sample of 10 students from this population, the mean and the standard deviation of students in the sample who have an iPhone is:
A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval (rounded up to 2 decimal values) for the population mean would equal:
Let the random variable X represent the score of a random student on a 'Test of Basic Skills'. Assume that X is a Normal with mean 6.8 and standard deviation 1.6. What is Pr(x > 9)?
A random sample size 20 taken from a normally distributed population resulted in a sample variance of 32. The lower limit of a 90% confidence interval for the population variance (rounded up to 3 decimal values) would be: