4. A rocking horse has a weight limit of 60 pounds<br><br> What weight is 95% of the limit?

The attention span of children (ages 3 to 5) is claimed to be Normally distributed with a mean of 15 minutes and a standard devi

Agata [3.3K]

Answer:

If the observed sample mean is greater than 17.07 minutes, then we would reject the null hypothesis.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 15 minutes

Sample size, n = 10

Alpha, α = 0.05

Population standard deviation, σ = 4 minutes

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 15\text{ minutes}\\H_A: \mu > 15\text{ minutes}$

Since the population standard deviation is given, we use one-tailed z test to perform this hypothesis.

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Now, $z_{critical} \text{ at 0.05 level of significance for one tail} = 1.64$

Thus, we would reject the null hypothesis if the z-statistic is greater than this critical value.

Thus, we can write:

$z_{stat} = \displaystyle\frac{\bar{x} - 15}{\frac{4}{\sqrt{10}} } > 1.64\\\\\bar{x} - 15>1.64\times \frac{4}{\sqrt{10}}\\\bar{x} - 15>2.07\\\bar{x} > 15+2.07\\\bar{x} > 17.07$

Thus, the decision rule would be if the observed sample mean is greater than 17.07 minutes, then we would reject the null hypothesis.

6 0

3 years ago

X^2-18x=-72<br><br> I need two solutions. Thanks.

eimsori [14]

Hey Astute!

Solve: x^2 - 18x = -72

Solution:

x^2 − 18x − (−72) = −72 − (−72) (Subtract -72 from both sides of the equation)

x^2 − 18x + 72 = 0

(x − 6) (x − 12) = 0 (Factor left side)

x − 6 = 0 or x − 12 = 0 (factors have to equal 0)

6 - 6 = 0 or 12 - 12 = 0

Answer:

x = 6 or x = 12

Hope This Helps, Have a Great Day!

7 0

2 years ago

Read 2 more answers

A convenience store manager notices that sales of soft drinks are higher on hotter days, so he assembles the data in a table, sh

Contact [7]

The regression equation to predict the number of cans sold on a day that is 90°F will be 871.

<h3>What is the linear system?</h3>

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

A convenience store manager notices that sales of soft drinks are higher on hotter days, so he assembles the data in the table, shown above. Use technology to find the equation of the least-squares regression line.

Then the regression line will be passing through (55, 340) and (84, 780). Then we have

y - 340 = 15.17(x - 55)

Then the regression equation to predict the number of cans sold on a day that is 90°F will be

y - 340 = 15.17 (90 - 55)

y = 871

More about the linear system link is given below.

brainly.com/question/20379472

#SPJ1

3 0

2 years ago

Mrs. Hawk assigns her students an average of no more than 5 questions on each assignment. On their first 5 assignments Mrs. Hawk

bixtya [17]

Given that <span>Mrs. Hawk assigns her students an average of no more than 15 questions on each assignment. On their first 5 assignments Mrs. Hawk’s students had 11, 10, 13, 14, and 14 questions.

Let x be the number of questions she can have on the sixth assignment, then the inequality that Mrs. Hawk can use to determine the number of questions she can have on the sixth assignment is given by

$\frac{11+10+13+14+14+x}{6} \leq15 \\ \\ \Rightarrow62+x\leq90 \\ \\ \Rightarrow x\leq28$ </span>

5 0

3 years ago

one serving of scrambled eggs contains 7.8 grams of fat. Mr.Jensen is trying to eat no more than 60 grams of fat per day.if he e

alexira [117]

Well you want to do 7.8 divided by 2 which is 3.9. Then you add that to 7.8 to signify that is it 1 1/2 which is 11.7. You subtract that from 60 and you get 48.3 and that is your answer

6 0

3 years ago

4. A rocking horse has a weight limit of 60 pounds What weight is 95% of the limit?