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3 years ago

10

Mrs. Sanchez is given a $550 hiring bonus with a new job. She earns an average commission of $275 per week for the year. If $68

is subtracted each week for taxes and benefits, how much does she earn in commissions and bonus for the year?

1 answer:

svetoff [14.1K]3 years ago

6 0

Mrs. Sanchez will earn $10,764

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A random sample of 864 births in a state included 426 boys. Construct a 95% confidence interval estimate of the proportion of bo

oksian1 [2.3K]

Using the z-distribution, it is found that the 95% confidence interval is (0.46, 0.526), and it does not provide strong evidence against that belief.

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which:

$\pi$ is the sample proportion.

z is the critical value.

n is the sample size.

In this problem, we have a 95% confidence level, hence $\alpha = 0.95$ , z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$ , so the critical value is z = 1.96.

We have that a random sample of 864 births in a state included 426 boys, hence the parameters are given by:

$n = 864, \pi = \frac{426}{864} = 0.493$

Then, the bounds of the interval are given by:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.493 - 1.96\sqrt{\frac{0.493(0.507)}{864}} = 0.46$

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.493 + 1.96\sqrt{\frac{0.493(0.507)}{864}} = 0.526$

The 95% confidence interval estimate of the proportion of boys in all births is (0.46, 0.526). Since the interval contains 0.506, it does not provide strong evidence against that belief.

More can be learned about the z-distribution at brainly.com/question/25890103

4 0

2 years ago

A contractor is required by a county planning department to submit one, two, three, four, five, or six forms (depending on the n

Ratling [72]

Answer:

a)

$k = \dfrac{1}{21}$

b) 0.476

c) 0.667

Step-by-step explanation:

We are given the following in the question:

Y = the number of forms required of the next applicant.

Y: 1, 2, 3, 4, 5, 6

The probability is given by:

$P(y) = ky$

a) Property of discrete probability distribution:

$\displaystyle\sum P(y_i) = 1\\\\\Rightarrow k(1+2+3+4+5+6) = 1\\\\\Rightarrow k(21) = 1\\\\\Rightarrow k = \dfrac{1}{21}$

b) at most four forms are required

$P(y \leq 4) = \displaystyle\sum^{y=4}_{y=1}P(y_i)\\\\P(y \leq 4) = \dfrac{1}{21}(1+2+3+4) = \dfrac{10}{21} = 0.476$

c) probability that between two and five forms (inclusive) are required

$P(2\leq y \leq 5) = \displaystyle\sum^{y=5}_{y=2}P(y_i)\\\\P(2\leq y \leq 5) = \dfrac{1}{21}(2+3+4+5) = \dfrac{14}{21} = 0.667$

8 0

3 years ago

Place the circles in order from the circle with the largest area to the circle with the smallest area.

11111nata11111 [884]

Answer:

Diameter 16, radius 7, circumference 37.68, diameter 8

Step-by-step explanation:

Largest area will be in a circle with the largest radius. So let's find all radii.

d = 8, so r = 4;

r = 7;

circumference = 2pi*r = 37. 68, so r = 6

diameter 18, so r = 8

5 0

3 years ago

Every 3 months the arena’s musical equipment needs safety checking. Look at a comparison of the last 4 years’ service costs.

shtirl [24]

The cheapest service would be the year in which the mean was the lowest. In Year 4, the mean was the lowest.

The most consistent service would be the year in which the range was the lowest. In Year 3, the range was the lowest.

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3 years ago

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What is a situation in which you would use fractions to express a number less than 1? What is a situation in which decimals seem

Semmy [17]

so you can not make the number smaller or reduce the fraction

ex.u can not simplify 11 over 12 because 11 is a prime number

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3 years ago