suppose that 60% of all students currently enrolled at all California Community College campuses combined are female. Researchers want to do a survery, and randomly select 1000 students who are currently enrolled at CSU campuses. Let P represent the proportion of students in the sample who are female. d. find the probability that more than 65% in the sample are female. Use the distribution Pe. find the probability that between 56% and 64% in the sample are female. Use the distribution Pf. repreat part (e), but use the Normal approximation to the binomial without  making the continuity correction. Show your calculator input and calculations or reasoning

Question
Asked Oct 7, 2019

suppose that 60% of all students currently enrolled at all California Community College campuses combined are female. Researchers want to do a survery, and randomly select 1000 students who are currently enrolled at CSU campuses. Let P represent the proportion of students in the sample who are female.

 

d. find the probability that more than 65% in the sample are female. Use the distribution P

e. find the probability that between 56% and 64% in the sample are female. Use the distribution P

f. repreat part (e), but use the Normal approximation to the binomial without  making the continuity correction. Show your calculator input and calculations or reasoning

check_circle

Expert Answer

Step 1

It is provided that P is defined as the proportion of students in the sample who are female. The proportion of females, who are enrolled in California Community college campuses, is 60%.

Proportion (p) 0.60
Sample size (n)
1000
Thus,
P Binomial (1000, 0.60)
Since the sample (n) is large, P will follow Normal distribution
Thus
Р(1-р)
P N p
п
help_outline

Image Transcriptionclose

Proportion (p) 0.60 Sample size (n) 1000 Thus, P Binomial (1000, 0.60) Since the sample (n) is large, P will follow Normal distribution Thus Р(1-р) P N p п

fullscreen
Step 2

d)

The probability, that more than 65.00% of the students in the sample are females, can be calculated as:

P-
Pr(P 0.65) Pr
0.65-0.60
0.0155
Pr(Z 3.2258)
=0.0006
help_outline

Image Transcriptionclose

P- Pr(P 0.65) Pr 0.65-0.60 0.0155 Pr(Z 3.2258) =0.0006

fullscreen
Step 3

e)

The probability, that more than 56.00% and less than 64.00% of the...

Pr(0.56 P<0.64)= Pr0.56-0.60 P- 0.64-0.60
0.0155
0.0155
Pr(-2.58 < Z< 2.58)
= Pr(Z < 2.58)-Pr(Z <-2.58)
=0.9951-0.0049
=0.9902
help_outline

Image Transcriptionclose

Pr(0.56 P<0.64)= Pr0.56-0.60 P- 0.64-0.60 0.0155 0.0155 Pr(-2.58 < Z< 2.58) = Pr(Z < 2.58)-Pr(Z <-2.58) =0.9951-0.0049 =0.9902

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Statistics

Other

Related Statistics Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: First Convert the following values into Z-scores. Then identify the proportion and probability in th...

A: a) Given data

question_answer

Q: I need help answering the following question using the data attached below: Create a histogram that ...

A: Enter the data of population as ashown below in excel

question_answer

Q: Before 1918, approximately 55% of the wolves in the New Mexico and Arizona region were male, and 45%...

A: (a)Calculations:Before 1918, there are approximately 55% of the wolves were male and 45% were female...

question_answer

Q: Suppose the speeds of vehicles traveling on a highway are normally distributed. If the population st...

A: Introduction:The 90% confidence interval for the population mean for given population standard devia...

question_answer

Q: Attendance at a university's basketball games follows a normal distribution with mean μ = 8000 and s...

A:  If a random variable x has a distribution with mean µ and standard deviation σ, then the z-score is...

question_answer

Q: 5. Suppose that you have a sample of 500 observations on two random variables: price denoted as X, a...

A: Consider, X and Y are the random variables which represent the price and profit respectively.Number ...

question_answer

Q: Here is a data set: 33 67 53 42 31 67 41 47 41 42 44 45 34 49 64 30 48 41 51 34 46 39 53 ...

A: The stem and leaf plot for the data is obtained from MINITAB software and given below.

question_answer

Q: Having trouble with c.

A: Introduction:If X ~ Bin (n, p), then the probability mass function of X is:p (x) = (nCx) px (1 – p)n...

question_answer

Q: nment: Applications X X + ses/48615/assignments/15888927module item id-6411020 eol G urse Home Page ...

A: The probability that a randomly selected bag of green will weigh less than 26 kilograms is 0.0099 an...