How do I simplify 355/10

Suppose a professional golfing association requires that the standard deviation of the diameter of a golf ball be less than 0.00

Bingel [31]

Answer:

We conclude that the standard deviation of the diameter of a golf ball is less than 0.005 inch.

Step-by-step explanation:

We are given that a professional golfing association requires that the standard deviation of the diameter of a golf ball be less than 0.005 inch.

Assume that the population is normally distributed: 1.678, 1.681, 1.676, 1.684, 1.676, 1.679, 1.681, 1.681, 1.677, 1.676, 1.681, 1.683.

Let $\sigma$ = population standard deviation of the diameter of a golf ball.

SO, Null Hypothesis, $H_0$ : $\sigma \geq$ 0.005 inch {means that the standard deviation of the diameter of a golf ball is more than or equal to 0.005 inch}

Alternate Hypothesis, $H_0$ : $\sigma$ < 0.005 inch {means that the standard deviation of the diameter of a golf ball is less than 0.005 inch}

The test statistics that would be used here One-sample Chi-square test statistics;

T.S. = $\frac{(n-1)s^{2} }{{\sigma^{2} }}$ ~ $\chi^{2} __n_-_1$

where, s = sample standard deviation = $\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }$ = 0.00281 inch

n = sample size = 12

So, the test statistics = $\frac{(12-1)\times 0.00281^{2} }{{0.005^{2} }}$ ~ $\chi^{2} __1_1$

= 3.47

The value of chi-square test statistics is 3.47.

Also, the P-value of test statistics is given by the following formula;

P-value = P( $\chi^{2} __1_1$ < 3.47) = 0.0182

Since, the P-value of the test statistics is less than the level of significance as 0.0182 < 0.05, so we reject our null hypothesis.

Now, at 0.05 significance level the chi-square table gives critical value of 4.575 at 11 degree of freedom for left-tailed test.

Since our test statistic is less than the critical value of chi-square as 3.47 < 4.575, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the standard deviation of the diameter of a golf ball is less than 0.005 inch.

7 0

3 years ago

Mast 1 broadcasts radio signals that can be heard within a radius of 15 km.

Alex73 [517]

Answer:

do your self it is easy

Step-by-step explanation:

do your self it is easy

8 0

3 years ago

1) An i staircase has a 10 inch vertical rise per step to get to the second floor of the house. If the angle of elevation is 30.

bezimeni [28]

Answer:

A)

Each landing is about 17 inches.

B)

The vertical rise from Floor 1 to Floor 2 is about 7 feet.

Step-by-step explanation:

Please refer to the attachment below. (I accidentally wrote 30.30 instead of 30.20. Please ignore that and sorry for any confusion.)

Part A)

So, we want to find the length of $\ell$ .

Note that the angle of elevation, the vertical height, and $\ell$ form a right triangle.

Since the vertical height opposite to our angle is 10, and we want to find the adjacent height, we can use the tangent ratio:

$\displaystyle \tan(x^\circ)=\frac{\text{Opposite}}{\text{Adjacent}}$

Therefore:

$\displaystyle \tan(30.20)=\frac{10}{\ell}$

Solve for $\ell$ . Cross-multiply:

$\displaystyle \ell\tan(30.20)=10$

So:

$\displaystyle \ell=\frac{10}{\tan(30.20)}=17.1817...\approx17\text{ inches}$

The landing space per step is about 17 inches.

Part B)

We know that there are a total of 12 feet of horizontal space total for each landing.

12 feet is equivalent to (12)(12) = 144 inches.

Since each landing is 17.1817... inches, this means that we have 144/(17.1817...) = 8.38... or about 8 steps.

Since the vertical rise of each step is 10 inches, the vertical rise from the 1st Floor to the second will be 8(10) or 80 inches or 80/12 = 6.666... or about 7 feet.