Skip to main content

How would you solve this stat problem without the calculator?

Hi, my teacher only teaches us how to solve problems using a calculator, but I want to learn how to solve this one by hand. I used the normal cumulative distribution function (CDF) for this question: A simple random sample (SRS) of 400 American adults is asked, "What do you think is the most serious problem facing our schools?" Suppose that, in fact, 30% of all adults would respond "drugs" if asked this question. The sample proportion, denoted as p-hat, will vary in repeated sampling. We can assign probabilities to different values of p-hat using the normal density curve with a mean of 0.3 and a standard deviation of 0.023.

Using this density curve, I need to find the probabilities for the following events: a) At least half of the sample believes that drugs are the most serious problem facing schools. b) Less than 25% of the sample believes that drugs are the most serious problem. c) The sample proportion is between 0.25 and 0.35.

I obtained the following results using a calculator: a) normalcdf(0.5, 1, 0.3, 0.023) = 1.7^-18 b) normalcdf(0, 0.25, 0.3, 0.023) = 0.015 c) normalcdf(0.25, 0.35, 0.3, 0.023) = 0.97.

Could someone please show me how to solve this by hand? I read that I need to use the z-score and other concepts, but I would appreciate a detailed explanation. Thank you!

1 Answers

A
Anonymous

Jan 29, 2025

a) At least half of the sample believes that drugs are the schools' most serious problem. normalcdf(0.5,1,0.3,0.023)=1.7^-18

P(X ≥ 0.5) = P((X - 0.3)/0.023 ≥ (0.5 - 0.3)/0.023) = P(Z ≥ 8.69) = P(Z ≤ - 8.69) = 0

b) normalcdf(0,0.25,0.3,0.023)=0.015

P(X ≤ 0.25) = P((X - 0.3)/0.023 ≤ (0.25 - 0.3)/0.023) = P(Z ≤ - 2.17) = 0.015003

c)The sample proportion is between 0.25 and 0.35.

P(0.25 ≤ X ≤ 0.35) = P((0.25 - 0.3)/0.023 ≤ (X - 0.3)/0.023 ≤ (0.35 - 0.3)/0.023) =

P( - 2.17 ≤ Z ≤ 2.17) = P(Z ≤ 2.17) - P(Z ≤ - 2.17) = 0.984997 - 0.015003 = 0.969994

Want to answer this question?

Join our community to share your knowledge!

Related Questions

3
Another expression for “it is raining” is “Está nublado.”

Question 1 (Yes/No Worth 1 point): Another expression for "it is raining" is "Está nublado." (Yes/No) Question 3 (Fill-i...

1
Guys help please!! Just 1 Algebra 2 question?

I need assistance with an Algebra 2 problem. The question states that the variable ( r ) varies directly with ( s ) and...

2
how is Frank Garza’s Jockey School?

I hope this message finds you well. I have a few questions regarding Frank Garza’s Jockey School. I want to clarify that...

8
I am in 12th……I hav my physics board exam tomorrow……how do I complete my full course in one day ?

I'm in 12th grade, and I have my physics board exam tomorrow. How can I effectively cover the entire course material in...

6
projectile motion homework?

A rescue pilot needs to drop a survival kit while flying at an altitude of 2,000.0 meters with a forward velocity of 100...

10
Preschool vs. Montessori?

Hi everyone, I’m trying to make a decision between enrolling my child in a preschool or a Montessori program. He’s curr...

3
what is the hybridization of phosphorus atom in PCl3?

What is the hybridization of the phosphorus atom in PCl3? Additionally, could you please provide an explanation of the s...

4
What should I wear for Home Depot orientation tomorrow?

I just got hired for a part-time sales job at Home Depot, and I have my orientation tomorrow. I've never had a job where...

7
Which view in a presentation program displays your slides in full-screen mode?

What view in a presentation program allows you to display your slides in full-screen mode?

2
why do african american kids score worse on the sat tests than whites or asians, regardless of their socioeconomic background?

What factors contribute to the observed differences in SAT scores among African American students compared to their Whit...