The sick days of employees every two years in a company are normally distributed with a population standard deviation of 7 days and an unknown population mean. If a random sample of 20 employees is taken and results in a sample mean of 21 days, find a 95% confidence interval for the population mean.

Step-by-step explanation:

Let [tex]$X_1, X_2, X_3,$[/tex] . . . ,Xn be the random sample of n employee's sick days. It is given that the random samples follows the  Normal distribution along with standard deviation of 7 days. Let

[tex]X_i\sim N(\mu ,7)[/tex]

[tex]\bar{X} =\frac{1}{n}\Sigma X_i\sim N(\mu,\frac{7}{\sqrt n})[/tex]

or   [tex]Z=\frac{\bar{X}-\mu}{7 /\sqrt n} \sim N(0,1)[/tex]

So,

[tex]P(-Z_{\alpha /2} \leq Z\leq Z_{\alpha /2} ) = 1- \alpha[/tex]

[tex]P(-Z_{\alpha /2} \leq \frac{\bar{X}- \mu}{7 / \sqrt n}\leq Z_{\alpha /2} ) = 1- \alpha[/tex]

[tex]P(\bar{X}-\frac{7}{\sqrt n} Z_{\alpha / 2} \leq \mu \leq \bar{X}+\frac{7}{\sqrt n} Z_{\alpha / 2} ) = 1- \alpha[/tex]

Therefore, the confidence interval of the population mean for α = 0.05 is

= [tex]P(\bar{X}-\frac{7}{\sqrt n} Z_{\alpha / 2} , \bar{X}+\frac{7}{\sqrt n} Z_{\alpha / 2} )[/tex]

= [tex]P(21-\frac{7}{\sqrt 20} Z_{0.05 / 2} , 21+\frac{7}{\sqrt 20} Z_{0.05 / 2} )[/tex]

= (17.93, 24.07)

If random variable X has a binomial distribution with n=15 and P(success) =p= 0.6, find the mean of X. That is, find E(X). Round to the whole number. Do not use decimals. Answer:

A bus makes a stop at 2:30 letting off 12 people

Four sisters buy a total of 3 1/2 feet of ribbon . The sisters want to share the ribbon equally how many feet of ribbon will each sister receive? 3/8 ft , 1/4 ft,1/2 ft, 7/8 ft

the circumference of a new P205/70R16 tires is 85.66in. if the old factory installed tires had a circumfrense of 72.13 in find the ratio

Find x so the distance between the points (x,2) and (-1,-2) is [tex]2\sqrt{5}[/tex]

x =_____ , ______

Can someone Identify the terms and coefficients;

8x-20y-10

Martina and Karina each wrote a number pattern on a strip of paper for each other to figure out. Find the next two numbers in Martina's number pattern. Describe the pattern and explain how you found it. 2, 6, 10, 14, ...​

What are the coordinates of the image of (- 4, 5) under the translation (x,y) (x-3,y+5)

you can afford a $250 per month car payment. you've found a 3 year loan at 2% interest . how big of a loan can you afford

Simplify: 6 (4x - 5)

Create a one-to-one function.

Figure STOP is reflected about the y-axis to obtain figure STO′P: A coordinate plane with two quadrilaterals is shown. Figure STOP has vertices S at negative 2 comma negative 1, T at negative 1 comma negative 4, O at negative 4 comma negative 5, and P at negative 5 comma negative 4. Figure S prime T prime O prime P prime has vertices S prime at 2 comma negative 1, T prime at 1 comma negative 4, P prime at 5 comma negative 4, and O prime at 4 comma negative 5. Which statement best describes the relationship between the two figures? (4 points) The measure of angle S is equal to the measure of angle P′. The measure of angle P is equal to the measure of angle T′. Figure STOP is congruent to figure S′T′O′P′.

An executive committee consists of 15 members: 7 men & 8 women. 5 members are selected at random to attend a meeting in Hawaii. The names are drawn from a hat. What’s the probability that all 5 selected are women?

Need help on this question

Is 0.843 less than 0.846

5.4 inches of snow fell in 3.6 hours. How much snow fell per hour?

2. In a survey of 1000 citizens in Seattle, Washington, 570 said they would pay higher prices in order to reduce greenhouse emissions. City planners conclude that between 55-59% of all Seattle citizens would do so.

a. What is the sample here? And what is the population? (1pts)

b. Is this a descriptive or a statistical inference? Why?

In a particular town, 20% of the homes have monitored security systems. If an alarm is triggered, the security system company will contact the local police to alert them of the alarm. Of all the alarm calls that the local police receive, they only have the manpower to answer 30% of the calls. Suppose we randomly sample one home that was broken into over the last month from this town. What is the probability that this home has a monitored security system and that the police answered the alarm call?

The function g(x) is graphed below. Find g(2).* N 22 need help solving please ​

The equation A=1250(1.03)^7 is being used to calculate the amount of money in a savings account. What does the 1.03 represent in this equation?

Write an equation for the parent function y = x^ 2 stretched by a factor of 6 and shifted down 4 units?

A certain medicine is given in an amount proportional to a patient's body weight. Suppose a patient weighing 162 pounds requires 216 milligrams of medicine.
What is the weight of a patient who requires 220 milligrams of medicine?

Maggie's brother is 10 years younger than three times her age. The sum of their ages is 50. How old is Maggie?

Maggie is _____ Years old

help help help help ​

Find the product of the complex number and its conjugate. 3 + 3i
18
9 - 9i
0
9 + 9i

rachel is setting up for her birthday . rachel wants to put the same number of chairs around each table . how many chairs will rachel place around each table at her birthday party ?

choices
3
4
5
6​

The ratio of dogs to cats at a veterinarians office is 5 to 3 if there are 15 cats how many total animals are at the office

I need to find the area below!
HELP!

What is the value of x that satisfies the equation 4/3=x+10/15

​Kirk's goal was to save​ $300 for a trip. In the first​ week, Kirk saved​ $16 from his allowance and​ $54 from his job. He spent​ $5 for lunch one day and another​ $2 on the bus. The second​ week, Kirk saved​ $62 and another​ $41 but spent​ $2 for the bus and​ $4 for lunch. How much money did Kirk save after 2​ weeks? Choose the correct answer below and fill in the answer box to complete your choice.