Ch 5 - Discrete Probability Distributions Ch 6 - Normal Distributions

The variance of a binomial distribution is given by (5.5) SD?

Variance (SD^2) = npq SD = SQRT(npq)

The mean of a binomial distribution is given by (5.5)

mean = np

The average number of miles driven on a full tank of gas in a certain model car before its​ low-fuel light comes on is 305. Assume this mileage follows the normal distribution with a standard deviation of 28 miles. (6.3) d. What is the probability​ that, before the​ low-fuel light comes​ on, the car will travel exactly 299 miles on the next tank of​ gas?

0 , instead of using FALSE in the NORM.DIST function (which will still give you a value) the answer is 0 because there is no area under the curve at this point)

In La Poisson distribution, the mean = variance, so how do you calculate the SD? (5.9)

variance, SQRT(variance)

One​ season, the average little league baseball game averaged 2 hours and 47 minutes ​(167 ​minutes) to complete. Assume the length of games follows the normal distribution with a standard deviation of 16 minutes. Complete parts a through d below. (6.4) d. What is the completion time in which 90​% of the games will be​ finished?

x = $187.5 x = mean + zSD =NORM.S.INV(0.9) = 1.2816 16*(1.2816) + 167

The average income tax refund for the 2009 tax year was ​$2948. Assume the refund per person follows the normal probability distribution with a standard deviation of ​$925. Complete parts a through d below. (6.5) b. What is the probability that a randomly selected tax return refund will be between ​$1500 and ​$2600​? c. What is the probability that a randomly selected tax return refund will be between ​$3200 and ​$4300​?

z = x - mean / SD*************** =NORM.S.DIST(z1, TRUE) -NORM.S.DIST(Z2, TRUE)

Consider a binomial probability distribution with p=0.3 and n=8. What is the probability of the​ following? (5.4) ​a) exactly three successes b) P(X<3) c) P(C>=5)

a) =BINOM.DIST(3, 8, 0.3,FALSE) b) =BINOM.DIST(2, 8, 0.3,TRUE) c) 1 - BINOM.DIST(5, 8, 0.3,TRUE)

Typically when distribution related questions are asking for a probability LESS than you _______________ if it is asking for GREATER than some x value you ____

=BINOMDISTRIBUTION 1-BINOMDISTRIBUTION

Which 2 formulas are commonly used with the normal distribution?

=NORM.S.DIST =NORM.DIST

For the normal distribution: (6.1) P(-0.88 <= z <= 1.78​)=

=NORM.S.DIST(1.78,TRUE) - NORM.S.DIST(-0.88,TRUE)

Consider a Poisson probability distribution with lambda=4.1 Determine the following probabilities: (5.8) ​ a) exactly 5 occurrences ​b) more than 6 occurrences ​c) 3 or fewer occurrences

a) =POISSON.DIST(5, 4.1, FALSE) b) =1-POISSON.DIST(6, 4.1,TRUE) c) =POISSON.DIST(3, 4.1, TRUE)

How would you create a histogram for this binomial probability distribution? (5.6)

Line up x (1-n) =BINOM.DIST(B10, 11, 0.3,FALSE) =BINOM.DIST(B10, 11, 0.3, TRUE) The nth (final) row should show 1 in the y column

The SD is simply the ________________________

SQRT of the variance

The SD of a Discrete Probability function = (5.1)

Sum of ((Outcome - Mean)^2)* probability

The mean of a Discrete Probability function = (5.1)

Sum of (outcome*probability)

With =NORM.S.DIST =NORM.DIST and =EXPON.DIST we usually use (TRUE or FALSE)

TRUE