Need help on this one

Susan is taking Western Civilization this semester on a pass/fail basis. The department teaching the course has a history of pas

Volgvan

Answer:

a. P(n) = 0.85 * (0.15)^(n-1)

b. P(n=1) = 0.85

c. P(n= 2) = 0.1275

d. P(n≥3) = 0.0225

e. Expected number of attempts is 1.176

Step-by-step explanation:

a.

Given

p = success = 85% = 0.85

q = failure = 1 - q = 1 - 0.85 = 0.15

The results of passing/failing takes a Bernoulli distribution

Since, there are independent trials

The number of trials until the first successful event occurs is given by

P(n = k) = p . (1 - p)^(k-1)

P(n = k) = p.q^(k-1)

This is so because it is a Bernoulli distribution and it is modeled by a geometric distribution.

Substitute 0.85 for p

P(n) = 0.85 * (0.15)^(n-1)

b.

Given

n = 1

Using P(n=1) = 0.85 * (0.15)^(n-1)

P(1) = 0.85 * 0.15^(1-1)

P(1) = 0.85 * 0.15°

P(1) = 0.85 * 1

P(1) = 0.85

Therefore, the probability that Susan passes on the first try is 0.85.

c.

n = 2

Using P(n=2) = 0.85 * (0.15)^(2-1)

P(2) = 0.85 * 0.15^(2-1)

P(2) = 0.85 * 0.15¹

P(2) = 0.85 * 0.15

P(2) = 0.1275

Therefore, the probability that Susan passes on the first try is 0.1275

d.

We'll make use of the probability of Susan passing the course after an infinite number of trials is 1.

i.e.

P(n=1) + P(n=2) + P(n=3) + P(n=4) + ......... = 1 --- This is then simplified to

P(n=1) + P(n=2) + P(n≥3) = 1

P(n≥3) = 1 - P(n=1) - P(n=2)

P(n≥3) = 1 - 0.85 - 0.1275

P(n≥3) = 0.0225

Therefore, the probability that Susan needs at least 3 attempts to pass is 0.0225

e.

In (a) above, we explained that the distribution is modeled by an exponential distribution.

The Expected Value for this is inverse of p, where p = 0.85

So, E(n) = 1/p

E(n) = 1/0.85

E(n) = 1.176470588235294

E(n) = 1.176 --- Approximated

Hence the Expected number of attempts is 1.176

7 0

4 years ago

Cheryl is planning to go to a four-year college in two years. She develops a monthly savings plan using the estimates shown. Wha

Alik [6]

Answer:

$541.67 per month

Step-by-step explanation:

Tuition and other expenses = $8,250 per semester.

There are two semesters in a year

She has 4 years to spend

Total semester=4years*2semesters

=8 semesters

4 years in college which is a total of 8 semesters.

Total Tuition and other expenses = $8,250 * 8

= $66,000

She needs a total of $66,00 to complete her college

Assistance from parents=$15,000

Financial aid(per semester)=$4750

Total financial aid=$38,000

Total assistance=

Assistance from parents+ financial aid

=$15000+$38,000

=$53,000

Total savings=Total amount needed - Total assistance

=$66,000 - $53,000

=$13,000

She needs to save $13,000 in two years

There are 12 months in one year

2 years=2*12=24 months

Monthly savings=Total savings/24 months

=$13,000/24

=$541.666666

To the nearest cent

=$541.67

3 0

4 years ago

Please help!

olasank [31]

8x + 84 = 500
8x = 416
x = 52

So if he wants to earn more than 500 dollars, he needs to make more than 52 dollars a week.

3 0

3 years ago

Read 2 more answers

please help asap! jermiah takes a taxi home from the mall. The taxi company charges $3.00, the rest is in the picture.

goblinko [34]

2.50m + 3.00 = 24.25

6 0

3 years ago

Whats nine рlus ten ?

EleoNora [17]

Answer:

19

Step-by-step explanation:

9+10=19

7 0

3 years ago