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worty [1.4K]
3 years ago
10

HELP ME PLEASE!

Mathematics
1 answer:
shusha [124]3 years ago
4 0

Answer:

Part A) The probability is closer to 0, because is less than 50%

Part B) The probability is closer to 1, because is greater than 50%

Step-by-step explanation:

we know that

The probability of an event is the ratio of the size of the event space to the size of the sample space.  

The size of the sample space is the total number of possible outcomes  

The event space is the number of outcomes in the event you are interested in.  

so  

Let

x------> size of the event space

y-----> size of the sample space  

so

P=\frac{x}{y}

Part A) Is the probability of hitting the black circle inside the target closer to 0 or 1?

In this problem we have

x------> is the area of the black circle

y------> is the total area of the square target

<em>Find the area of black circle</em>

r=3/2=1.5\ units    

x=(3.14)(1.5)^{2} =7.065\ units^{2}

<em>Find the total area of the square target</em>

y=9^{2}=81\ units^{2}

Find the probability

P=\frac{7.065}{81}=0.0872

Convert to percentage

0.0872*100=8.72\%

The probability is closer to 0, because is less than 50%

Part B) Is the probability of hitting the white portion of the target closer to 0 or 1?

In this problem we have

x------> is the area of the white portion of the target

y------> is the total area of the square target

<em>Find the area of the white portion</em>

The area is equal to the area of the square minus the area of the circle

x=81-7.065=73.935\ units^{2}

Find the probability

P=\frac{73.935}{81}=0.9128

Convert to percentage

0.9128*100=91.28\%

The probability is closer to 1, because is greater than 50%

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The sugar content of the syrup in canned peaches is normally distributed. A random sample of n = 10 cans yields a sample standar
Serggg [28]

Answer:

The 95% confidence interval is given by:

3.30<σ<8.76

Step-by-step explanation:

1) Data given and notation

s=4.798 represent the sample standard deviation

\bar x represent the sample mean

n=10 the sample size

Confidence=95% or 0.95

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

df=n-1=10-1=9

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a tabel to find the critical values.  

The excel commands would be: "=CHISQ.INV(0.025,9)" "=CHISQ.INV(0.975,9)". so for this case the critical values are:

\chi^2_{\alpha/2}=19.022

\chi^2_{1- \alpha/2}=2.700

And replacing into the formula for the interval we got:

\frac{(9)(4.798)^2}{19.022} \leq \sigma \frac{(9)(4.798)^2}{2.700}

10.892 \leq \sigma^2 \leq 76.736

Now we just take square root on both sides of the interval and we got:

3.30 \leq \sigma \leq 8.76

So the best option would be:

3.30<σ<8.76

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Step-by-step explanation:

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So firstly, I'm going to be converting the mixed number into an improper fraction. To do this, multiply the whole number by the denominator and then add that product with the numerator and that will be your new numerator. In this case:

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