In: Statistics and Probability

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 student is female and dropped out?

(d) Given that the student is female, what is the probability that she dropped out?

(e) Given that the student dropped out, what is the probability that the student is female?

A total of 23 Gossett High School students were admitted to
State University. Of those students, 7 were offered athletic
scholarships. The school’s guidance counselor looked at each
group’s summary statistics of their composite ACT scores, wondering
if there was a difference between the groups (those who were not
offered scholarships and those who were). The statistics for the 16
students who were not offered scholarships are x̅ = 24.7, s = 2.8
and for the 7 who were, x̅...

In a recent survey of high school students, it was found that
the amount of time spent on reading books per week was normally
distributed with a mean of 32 minutes. Assume the distribution of
weekly reading time follows the normal distribution with a
population standard deviation of 2 minutes. Suppose we select a
sample of 20 high school students.
a. What is the standard error of the mean time?
Answer
b. What percent of the sample means will be...

Imagine Penn State were to hold summer events for High school
students. Should it include freshman and sophomores? Or be open to
all high school students & their families titled "College 101."
What should Penn State do? What do families and students need to
know at that point in their highschool to start considering? Who
should they listen to? What do you wish you would have known then
to help set you up for success? Would a panel discussion be...

Last year, 30% of high school students in a particular county
were able to find a summer job. A county official wants to estimate
this quantity again this year. She wants to be 95% confident that
the margin of error is no larger than 2%. Find the smallest sample
size that would allow the official to achieve her goals.
a.
21
b.
2017
c.
10
d.
474

In a recent year, grade 6 Michigan State public school students
taking a mathematics assessment test had a mean score of 303.1 with
a standard deviation of 36. Possible test scores could range from 0
to 1000. Assume that the scores were normally distributed.
a) Find the probability that a student had
a score higher than 295.
b) Find the probability that a student had a
score between 230 and 305.
c) What is the highest score that would still place...

After the recent school shooting in Florida, high school
students have led the protests demanding stricter gun laws. After
the Treyvon Martin shooting five years ago, young people started
the Black Lives Matter movement. Based on emotional and social
development in adolescence, why do you think these young people
were the ones to work for change?

Fifteen students from Poppy High School were accepted at Branch
University. Of those students, six were offered academic
scholarships and nine were not. Mrs. Bergen believes Branch
University may be accepting students with lower ACT scores if they
have an academic scholarship. The newly accepted student ACT scores
are shown here.
Academic scholarship: 25, 24, 23, 21, 22, 20
No academic scholarship: 23, 25, 30, 32, 29, 26, 27, 29, 27
Part A: Do these data provide convincing evidence
of...

Twenty students from Sherman High School were accepted at
Wallaby University. Of those students, eight were offered military
scholarships and 12 were not. Mr. Dory believes Wallaby University
may be accepting students with lower SAT scores if they have a
military scholarship. The newly accepted student SAT scores are
shown here.
Military scholarship: 850, 925, 980, 1080, 1200, 1220, 1240,
1300
No military scholarship: 820, 850, 980, 1010, 1020, 1080, 1100,
1120, 1120, 1200, 1220, 1330
Part A: Do these...

Twenty-five students from Harry High School were accepted at
Magic University. Of those students, 10 were offered athletic
scholarships and 15 were not. Mrs. Hermione believes Magic
University may be accepting people with lower ACT scores if they
are athletes. The newly accepted student ACT scores are shown here.
Athletic scholarship: 16, 24, 20, 25, 24, 23, 21, 22, 20, 20 No
athletic scholarship: 23, 25, 26, 30, 32, 26, 28, 29, 26, 27, 29,
27, 22, 24, 25 Part...

In a recent survey of county high school students, 100 males and
100 females, 66 of the male students and 47 of the female students
sampled admitted that they consumed alcohol on a regular basis.
Find a 90% confidence interval for the difference between the
proportion of male and female students that consume alcohol on a
regular basis. Can you draw any conclusions from the confidence
interval?
For the test of significance questions, clearly indicate each of
the formal steps...

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