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3 years ago

11

A true/false test consists of 25 questions. A student knows the correct answer to 10 of the questions. She guesses each of the o

ther answers independently based on the toss of a coin. a) Find the expectation of the number of correct answers.

1 answer:

babunello [35]3 years ago

4 0

Answer:

The expectation of the number of correct answers is 17.5

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the student guesses it correctly, or he does not. The probability of a student guessing the answer of a question correctly is independent of other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

$E(X) = np$

In this problem, we have that:

25 questions.

The student know the answer for 10 questions. So for these 10 questions, p = 1.

On the other 25-10 = 15, she will guess, which there is one correct answer out of 2 options(true/false), so p = 1/2 = 0.5. So

$E(X) = 10*1 + 15*0.5 = 17.5$

The expectation of the number of correct answers is 17.5

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Read 2 more answers

Snow Dome Ski Resort has 75 inches of snow. It is currently snowing there at a rate of 1 inch per hour. Mt. Winterpark Ski Resor

Nastasia [14]

Answer:

a. See explanation for table

b. The 7th hour

Step-by-step explanation:

Given

Ski Resort

$Base\ Snow = 75in$

$Rate = 1in$ hourly

Mt. Winterpark

$Base\ Snow = 68in$

$Rate = 2in$ hourly

First, we need to illustrate the amount of snow as an equation in both cases.

$Amount = Base\ Snow + Rate * Time$

Let x be number of hours. and y be the amount of snow

So:

Ski Resort

$y= 75 + 1* x$

$y= 75 + x$

Mt. Winterpark

$y= 68 + 2 * x$

$y= 68 + 2x$

Next, we make a table to show the data.

When $x = 0$

Ski Resort: $y = 75 + 0 = 75$

Mt. Winterpark: $y = 68 + 2(0) = 68$

When $x = 1$

Ski Resort: $y = 75 + 1 = 76$

Mt. Winterpark: $y = 68 + 2(1) = 70$

When $x = 2$

Ski Resort: $y = 75 + 2 = 77$

Mt. Winterpark: $y = 68 + 2(2) = 72$

When $x = 3$

Ski Resort: $y = 75 + 3 = 78$

Mt. Winterpark: $y = 68 + 2(3) = 74$

When $x = 4$

Ski Resort: $y = 75 + 4 = 79$

Mt. Winterpark: $y = 68 + 2(4) = 76$

When $x = 5$

Ski Resort: $y = 75 + 5 = 80$

Mt. Winterpark: $y = 68 + 2(5) = 78$

When $x = 6$

Ski Resort: $y = 75 + 6 = 81$

Mt. Winterpark: $y = 68 + 2(6) = 80$

When $x = 7$

Ski Resort: $y = 75 + 7 = 82$

Mt. Winterpark: $y = 68 + 2(7) = 82$

When $x = 8$

Ski Resort: $y = 75 + 8 = 83$

Mt. Winterpark: $y = 68 + 2(8) = 84$

When $x = 9$

Ski Resort: $y = 75 + 9 = 84$

Mt. Winterpark: $y = 68 + 2(9) = 86$

When $x = 10$

Ski Resort: $y = 75 + 10 = 85$

Mt. Winterpark: $y = 68 + 2(10) = 88$

Hence, the table is:

x ---- Ski Resort ---- Mt. Winterpark

0 --------75 ----------- 68

1 --------76 ----------- 70

2 --------77 ----------- 72

3 --------78 ----------- 74

4 --------79 ----------- 76

5 --------80 ----------- 78

6 --------81 ----------- 80

7 --------82 ----------- 82

8 --------83 ----------- 84

9 --------84 ----------- 86

10 -------85 ----------- 88

(b)

From the table, the amount of snow is the same at the 7th hour and the snow is 82 inches

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3 years ago