Question

In: Statistics and Probability

a certain state has the highest high school graduation rate of all states at 80% A....

a certain state has the highest high school graduation rate of all states at 80%

A. In a random sample of 20 high school students from the state, what is the probability that 17 will graduate?

B. In a random sample of 20 high school students what is the probability that 16 or fewer will graduate?

C. What is the probability that at least 17 high school students in our sample of 20 will graduate?

Expert Solution

Here probability of high school graduation rate = p = 0.80

sample size = n= 20

as the events are independent and success rate is constant.

So here if x is the the number of graduates out of 20, so x will have binomial distribution with parameter n = 20 and p = 0.80

(A) So here the distribution

p(x) = ²⁰C_x (0.80)^x(0.20)^{(20 - x)}

p(x = 17) = ²⁰C₁₇(0.80)¹⁷(0.20)³ = 0.2054

(B) Probability that 16 or fewer willgraduate

Here we will use cumulative binomial function either in excel (BINOMDIST) or in TI-84 calculator (BINOMCDF)

Pr(x 16) = BINOMDIST(x 16;20 ;0.80) = 0.5886

(C) Probability that at least 17 high school studnets in our sample of 20 will graduuate.

Pr(x 17) = 1 - Pr(x 16)

Pr(x 17) = 1 - 0.5886 = 0.4114

orchestra answered 1 year ago

In some states, high school students must pass a graduation test before they are able to...

In some states, high school students must pass a graduation test before they are able to receive their high school diplomas. Suppose the students are given up to three chances to pass the exam. If they pass it, they don't need to take it again. If they do not pass the test on the first try, they take it a second time. If they don't pass on the second try, they take it a third time. From past data, we...

The linear regression equation for predicting poverty (%) from the high school graduation rate (%) is...

The linear regression equation for predicting poverty (%) from the high school graduation rate (%) is as follows: ˆ y = 29 -0.2*x High school graduation rate for North Carolina is 22% and the poverty rate is 29.5%. Find the residual for this observation (round your answer to one decimal place)

It is claimed that Florida’s high-school graduation rate is 77.9%. You take a random sample of...

It is claimed that Florida’s high-school graduation rate is 77.9%. You take a random sample of 300 Florida high-school seniors and discover that 41 of them withdrew during the year. At α=0.05, is there enough evidence to reject the claim?

What are some pyschological effects of high school graduation?

In a certain high school, uniforms are optional. A study shows that high school students who...

In a certain high school, uniforms are optional. A study shows that high school students who wear uniforms have a lower grade average than students who don't wear uniforms. From this study, the school administration claims that they should not require the students to wear uniforms because that is the cause of the lowering grades. Another possible explanation is that students who wear uniforms are poorer than the students who don't wear uniforms and the economic situation of their parents...

The school population for a certain school is predicted to increase by 80 students per year...

The school population for a certain school is predicted to increase by 80 students per year for the next 14 years. If the current enrollment is 800 students, what will the enrollment be after 14 years? Joe's annual income has been increasing each year by the same dollar amount. The first year his income was $24,700, and the 12th year his income was $37,900. In which year was his income $ 43,900? How many terms are there in each of...

1. a) Time Magazine states that the drop out rate for high school seniors is ten...

1. a) Time Magazine states that the drop out rate for high school seniors is ten percent. You conduct a test to see if the drop out rate for high school seniors is actually more than ten percent. One hundred high school seniors were randomly selected to see if they had dropped out. The number of these high school seniors who dropped out is 15. Determine the p-value using test statistic, z=1.67. Draw the graph. (α =0.01) b) Time Magazine states that the...

In a survey of 100 U.S. residents with a high school diploma as their highest educational...

In a survey of 100 U.S. residents with a high school diploma as their highest educational degree (Group 1) had an average yearly income was $35,621. Another 120 U.S. residents with a GED (Group 2) had an average yearly income of $33,498. The population standard deviation for both populations is known to be $4,310. At a 0.01 level of significance, can it be concluded that U.S. residents with a high school diploma make significantly more than those with a GED?...

b) A high-school student has a monthly budget of $80 to spend on music and burritos....

b) A high-school student has a monthly budget of $80 to spend on music and burritos. Burritos cost $8 each, while songs are free after paying the Spotify monthly fee of $9.99. 1. In a diagram, measuring songs along the horizontal axis, draw the high-school student’s budget constraint. c) A family has an yearly income of $50,000 to spend on the kids’ education or on all other goods. 1. In a diagram measuring dollars spent on education along the horizontal...

In a recent school year in the state of Washington, there were 319,000 high school students....

In a recent school year in the state of Washington, there were 319,000 high school students. Of these, 154,000 were girls and 165,000 were boys. Among the girls, 41,100 dropped out of school, and among the boys, 10,500 dropped out. A student is chosen at random. Round the answers to four decimal places. (a) What is the probability that the student is female? (b) What is the probability that the student dropped out? (c) What is the probability that the...