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3 years ago

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Question 13 pts

1 answer:

oee [108]3 years ago

7 0

Answer:

1. 68%

2. 50%

3. 15/100

Step-by-step explanation:

Here, we want to use the empirical rule

1. % waiting between 15 and 25 minutes

From what we have in the question;

15 is 1 SD below the mean

25 is 1 SD above the mean

So practically, we want to calculate the percentage between;

1 SD below and above the mean

According to the empirical rule;

1 SD above the mean we have 34%

1 SD below, we have 34%

So between 1 SD below and above, we have

34 + 34 = 68%

2. Percentage above the mean

Mathematically, the percentage above the mean according to the empirical rule for the normal distribution is 50%

3. Probability that someone waits less than 5 minutes

Less than 5 minutes is 3 SD below the mean

That is 0.15% according to the empirical rule and the probability is 15/100

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$\frac{1}{5} x - \frac{2}{3} y = 30 \\ \frac{1}{5} x - \frac{2}{3} 15 = 30 \\ \frac{1}{5} x - \frac{30}{3} = 30 \\ \frac{1}{5} x - 10 = 30 \\ \frac{1}{5} x = 30 + 10 \\ \frac{1}{5} x = 40 \\ x = 40 \div \frac{1}{5} \\ x = 40 \times \frac{5}{1} \\ x = 40 \times 5 \\ x = 200$

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$w = \dfrac{1 + 4\sqrt3\,i}4 = \dfrac74 \exp\left(i \tan^{-1}(4\sqrt3)\right)$

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Use de Moivre's theorem again to take square roots on both sides.

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2 years ago