MATH 1F92 Lecture 7: Math+1F92-+7.4-+Normal+Approximation+to+the+Binomial+Probability+Distribution+Fill+In

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cyanfly632

16 Feb 2017

School

Brock University

Department

Mathematics and Statistics

Course

MATH 1F92

Professor

dr.christina

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Document Summary

If you have (cid:370)n(cid:371) number of trials, with two outcomes (success or failure) that are mutually exclusive, and each trial is completely independent of the previous trial, then we have a binomial distribution. The probability of the random variable (cid:370)x(cid:371) having a total of (cid:370)x(cid:371) number of success is equal to: (cid:4666)=(cid:4667)=(cid:4672) (cid:4673)(cid:1868) (cid:4666)(cid:883) (cid:1868)(cid:4667) ) with a mean of: =(cid:1866)(cid:1868) and a standard deviation of:= (cid:1866)(cid:1868) (cid:4666)(cid:883) (cid:1868)(cid:4667) Example: a telemarketer has a 4 hour shift where they usually call about. = (cid:885)(cid:885)(cid:887) (cid:883)(cid:882) (cid:2875)+ (cid:887). (cid:888)(cid:889)(cid:889) (cid:883)(cid:882) (cid:2874) + 0. 000047 + 0. 000258 + 0. 001 + 0. 003. = 0. 0043 or 0. 43: find the probability of more than 5 people staying on the line during that time period. = 0. 9957% or 99. 57: find the probability that more than 32 of the calls stay on the line during that time period. In situations like part c, it will take us forever.

Related Questions

A salesperson makes four calls per year. A sample of 100 days given the following frequencies of sales volumes.

Number of Sales	Observed Frequency (days)
0	30
1	32
2	25
3	10
4	3
TOTAL	100

Records show sales are made to 30% of all sales calls. Assuming independent sales calls, the number of sales per day should follow a binomial distribution. The Binomial distribution is represented by:

For this exercise, assume that the population has a binomial probability distribution with n=4, p=0.30 and x= 0, 1, 2, 3 and 4.

(a) Compute the expected frequencies for x=0, 1, 2, 3 and 4 by using the binomial probability function. Combine categories if necessary to satisfy the requirement that the expected frequency is five or more for all categories.

(b) Use the goodness of fit test to determine whether the assumption of a binomial probability distribution should be rejected. Because no parameters of the Binomial probability distribution were estimated from the sample data, the degrees of freedom are k-1 .

whitebear607

Name polynomial by number of terms.

Place in standard form.

Name the degree and number of terms of the polynomial

A) second degree monomial

B) third degree polynomial with four terms

C) sixth degree monomial

D) sixth degree polynomial with four terms

Let X denote the number of Canon digital cameras sold during
a particular week by a certain store. The pmf of X is
x | 0 1 2 3 4
pX(x) | .1 .2 .3 .25 .15
Sixty percent of all customers who purchase these cameras
also buy an extended warranty. Let Y denote the number of
purchasers during this week who buy an extended warranty.

a. What is P(X =4, Y = 2)? [Hint: This probability equals
P(Y = 2 I X = 4) * P(X = 4); now think of the four purchases
as four trials of a binomial experiment, with success
on a trial corresponding to buying an extended warranty.]
b. Calculate P(X = Y).
c. Determine the joint pmf of X and Y and then the marginal
pmf of Y.

redgiraffe649

MATH 1F92 Lecture 7: Math+1F92-+7.4-+Normal+Approximation+to+the+Binomial+Probability+Distribution+Fill+In

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