section 5

.pdf

School

College of Southern Nevada *

*We aren’t endorsed by this school

Course

152

Subject

Statistics

Date

May 2, 2024

Type

pdf

Pages

Uploaded by ElderNeutronShark49 on coursehero.com

5.5 Normal Approximations to Binomial Distributions Definitions are in the textbook. Answers to Examples are on last page of these notes. Normal Approximation to a Binomial Distribution If np ≥ _____ and nq ≥ ______ then the binomial random variable x is approximately ____________________________ distributed, with mean: and standard deviation: where n is the number of independent ________________________, p is the probability of ______________________ in a single trial, and q is the probability of _____________________________ in a single trial. TRY IT YOURSELF 1 A binomial experiment is listed. Determine whether you can use a normal distribution to approximate the distribution of x, the number of people who reply yes. If possible, find the mean and standard deviation. If not, explain why. In a survey of teen drivers in the U.S., 35% admit to texting while driving. You randomly select 100 teen drivers in the U.S. and ask them whether they admit to texting while driving. Continuity correction -

TRY IT YOURSELF 2 Use a continuity correction to convert each binomial probability to a normal distribution probability. A. The probability of getting between 57 and 83 successes, inclusive. B. The probability of getting at most 54 successes. Complete the table below which shows how to convert binomial probabilities to a normal distribution probability. The first row is already done for you. Binomial Normal Notes Exactly c P(c - 0.5 < x < c + 0.5) Includes c At most c Fewer than c At least c More than c Guidelines to Using a Normal Distribution to Approximate Binomial Probabilities In Words In Symbols 1. Verify that a __________________________________ applies. 2. Determine whether you can use a ______________________ _____________________________________ to approximate x, the binomial variable. 3. Find the _________________ and _____________________________ ______________________________ for the distribution. 4. Apply the appropriate _______________________________ ___________________________. Shade the corresponding area under the ______________________________ __________________. 5. Find the corresponding _______________________________. 6. Find the ________________________________. TRY IT YOURSELF 3 in a survey of teen drivers in the US, 35% admit to texting while driving. You randomly select 100 teen drivers in the US and ask them whether they admit to texting while driving. What is the probability that more than 30 respond yes?

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Recommended textbooks for you

Calculus For The Life Sciences

Calculus

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:Pearson Addison Wesley,

SEE MORE TEXTBOOKS