Mathematics, 30.07.2020 18:01 skyhe34

Pat is taking an economics course. Pat's exam strategy is to rely on luck for the next exam. The exam consists of 100 true-false questions. Pat plans to guess the answer to each question without reading it. If a grade on the exam is 60% or more, Pat will pass the exam. Find the probability that Pat will pass the exam.

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Answer from: genesist720

The probability that Pat will pass the exam is 0.02775.

Step-by-step explanation:

We are given that exam consists of 100 true-false questions. Pat plans to guess the answer to each question without reading it.

If a grade on the exam is 60% or more, Pat will pass the exam.

Let X = grade on the exam by Pat

The above situation can be represented through binomial distribution such that X ~ Binom(n = 100, p = 0.50).

Here the probability of success is 50% because there is a true-false question and there is a 50-50 chance of both being the correct answer.

Now, here to calculate the probability we will use normal approximation because the sample size if very large(i.e. greater than 30).

So, the new mean of X, $\mu$ = $n \times p$ = $100 \times 0.50$ = 50

and the new standard deviation of X, $\sigma$ = $\sqrt{n \times p \times (1-p)}$

= $\sqrt{100 \times 0.50 \times (1-0.50)}$

= 5

So, X ~ Normal( $\mu=50, \sigma^{2} = 5^{2}$ )

Now, the probability that Pat will pass the exam is given by = P(X $\geq$ 60)

P(X $\geq$ 60) = P( $\frac{X-\mu}{\sigma}$ $\geq$ $\frac{60-50}{5}$ ) = P(Z $\geq$ 2) = 1 - P(Z < 2)

= 1 - 0.97725 = 0.02275

Hence, the probability that Pat will pass the exam is 0.02775.

Answer from: Quest

step-by-step explanation:

the denominator cannot be the same as one of the factors.

8 denominator times 2 denominator = 16

and 7 numerator time 11 = 77

77/16= 77/16 ( they cannot be further simplified)

Answer from: Quest

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9

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Pat is taking an economics course. Pat's exam strategy is to rely on luck for the next exam. The exa...