Normal distribution Flashcards
Symbols for normal distribution
μ is the mean
σ2 is the variance
σ is the standard deviation
The continuous random variable can follow a normal distribution if:
- The distribution is symmetrical
- The distribution is bell-shaped
When can I use a normal distribution to approximate a binomial distribution?
- n is large (large number of trials)
- p is close to 0.5
The mean and variance of a binomial distribution can be calculated by:
μ=np
σ^2=np(1-p)
How do I approximate a probability?
STEP 1: Find the mean and variance of the approximating distribution
STEP 2: Apply continuity corrections to the inequality
STEP 3: Find the probability of the new corrected inequality
Use the “Normal Cumulative Distribution” function on your calculator
The probability will not be exact as it is an approximate but provided n is large and p is close to 0.5 then it will be a close approximation
The records also show that the time, Q minutes, to ride 50km is normally distributed with mean 96 minutes and standard deviation 8 minutes. The club’s Captain would like to use these distributions to estimate the proportion of athletes from the club who can run 5km faster than 17 minutes and can cycle 50km in less than 1.5 hours. State a necessary assumption about R and Q for the Captain to calculate an estimate of
this proportion.
Need R and Q to be independent
or events {R < 18} and {Q < 90} are independent
