Let X be a Gaussian random variable with mean 10 and variance 4. A sample of size 9 is obtained and the sample mean, minimum, and maximum of the sample are calculated. (a) Find the probability that the sample mean is less than 9.
(b) Find the probability that the minimum is greater than 8.
(c) Find the probability that the maximum is less than 12.
(d) Find n so the sample mean is within 1 of the true mean with probability 0.95.
(e) Generate 100 random samples of size 9. Compare the probabilities obtained in parts a, b, and c to the observed relative frequencies.

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560

i don't see any

step-by-step explanation:

all of the measures need to be converted to the same measure; such as inches. if you do that it is easy to determine which is the longest, 2500 mm which is approximately 97.5 inches.