Which values best approximate the solutions of

Sodas in a can are supposed to contain an average 12 oz. This particular brand has a standard deviation of 0.1 oz, with an avera

hoa [83]

Answer:

The probability is $P(X < 12) = 0.99286$

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 12 \ oz$

The standard deviation is $\sigma = 0.1 \ oz$

The sample mean is $\= x = 12.1 \ oz$

The sample size is n = 6 packs

The standard error of the mean is mathematically represented as

$\sigma_{\= x } = \frac{\sigma}{\sqrt{n} }$

substituting values

$\sigma_{\= x } = \frac{0.1}{\sqrt{6} }$

$\sigma_{\= x } = 0.0408$

Given that the can’s contents follow a Normal distribution then then the probability that the mean contents of a six-pack are less than 12 oz is mathematically represented as

$P(X < 12) = P ( \frac{X - \mu }{ \sigma_{\= x }} < \frac{\= x - \mu }{ \sigma_{\= x }} )$

Generally $\frac{X - \mu }{ \sigma_{ \= x }} = Z (The \ standardized \ value \ of \ X )$

So

$P(X < 12) = P ( Z < \frac{\= x - \mu }{ \sigma_{\= x }} )$

substituting values

$P(X < 12) = P ( Z < \frac{12.2 -12 }{0.0408} )$

$P(X < 12) = P ( Z < 2.45 )$

From the normal distribution table the value of $P ( Z < 2.45 )$ is

$P (Z < 2.45)0.99286$

=> $P(X < 12) = 0.99286$

4 0

3 years ago

Please help me with all these questions . I really appreciate it but if you don't how to do it please comment don't answer the q

frozen [14]

For number 1, add the sides of the triangle. They are all given. The answer is 19.

For number 2, you use the formula for circumference, 2 times pi times radius. The answer is 43.96.

For number 3, I assume that 5 is half of one side. You would double 5 to get ten and multiply it by four, since there are four sides in a square. The answer is 40.

For number 4, you would multiply 5 times pi, but don't solve it. ( since the directions are to leave the answer in terms of pi) The answer is 5 pi.

For number 5, add all the sides together like number 1. The answer is 18.

8 0

3 years ago

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"Durable press" cotton fabrics are treated to improve their recovery from wrinkles after washing "Wrinkle recovery angle" measur

ludmilkaskok [199]

Answer:

At 5% there is significant evidence to reject the null hypothesis. You can conclude that there is a difference between the population mean of the wrinkle recovery angle of fabric treated with Permafresh and the population mean of the wrinkle recovery angle of fabric treated with Hylite.

a)

X[bar]₁= 120.8 degrees

X[bar]₂= 162.75 degrees

b)

S₁²= 14.5155 degrees

S₂²= 24.4727 degrees

Step-by-step explanation:

Hello!

The study variable is X: wrinkle recovery angle for a fabric specimen.

There is a suspicion that there is a difference in recovery from wrinkles after washing between two products (Permafresh and Hilite). To test this suspicion two random samples of fabric, 5 were treated with Permafresh and 4 were treated with Hylite resulting in the data:

Sample 1 (Permafresh)

X₁: wrinkle recovery angle for a fabric specimen treated with Permafresh.

X₁~N(μ₁;σ₁²)

n₁= 5

124; 104; 142; 111; 123

Sample mean X[bar]₁= (∑x₁i)/n₁= 604/5= 120.8 degrees

Sample variance S₁²= $\frac{1}{(n₁-1)}$ [(∑x₁²i)-(∑x₁i)²/n₁] = $\frac{1}{4}$ [(73806)-(604)²/5]= 210.7 degrees²

S₁= 14.515 ≅ 14.52 degrees

Sample 2 (Hylite)

X₂: wrinkle recovery angre for a fabric specimen trated with Hylite.

X₂~N(μ₂;σ₂²)

n₂= 4

147; 199; 149; 156

Sample mean X[bar]₂= (∑x₂i)/n₂= 651/4= 162.75 degrees

Sample variance S₂²= $\frac{1}{(n₂-1)}$ [(∑x₂²i)-(∑x₂i)²/n₂] = $\frac{1}{3}$ [(107747)-(651)²/4]= 598.916 ≅ 598.92 degrees²

S₂= 24.472≅ 24.47 degrees

To test the suspicion that there is a difference between the winkle recovery angle on fabric samples treated with Permafresh and Hylite, the hypothesis is:

H₀: μ₁ = μ₂

H₁: μ₁ ≠ μ₂

α: 0.05

To test the difference between the population means, considering that only sample information is available and the size of both samples, the most appropriate statistic to use is a pooled t for independent samples (unknown but equal population variances):

t= (X[bar]₁ - X[bar]₂) - (μ₁ - μ₂) ~t $_{n_1+n_2-2}$

Sa√(1/n₁+1/n₂)

Sa²= (n₁-1)S₁² + (n₂-1)S₂² = (4*210.7)+(3*598.92) = 377.08

n₁ + n₂ - 2 5+4-2

Sa= 19.418≅ 19.42

t= (X[bar]₁ - X[bar]₂) - (μ₁ - μ₂) = (120.8-162.75) - 0 = -3.22

Sa√(1/n₁+1/n₂) 19.42√(1/5+1/4)

Using the critical region approach, this rejection region is two-tailed with critical values:

$t_{n_1+n_2-2; \alpha/2 } = t_{7; 0.025 } = -2.365$

$t_{n_1+n_2-2; 1- \alpha/2 } = t_{7; 0.975 } = 2.365$

If t ≤ -2.365 or t ≥2.365, then the decision is to reject the null hypothesis.

If -2.365 < t < 2.365, then the decision is to not reject the null hypothesis.

Since the calculated t-value is less than the left critical value, the decision is to reject the null hypothesis.

I've calculated the p-value for the test: 0.0146

This p-value is less than the significance level of 0.05, then, using this approach, the decision is also to reject the null hypothesis.

This means, that at 5% there is significant evidence to reject the null hypothesis. You can conclude that there is a difference between the population mean of the wrinkle recovery angle of fabric treated with Permafresh and the population mean of the wrinkle recovery angle of fabric treated with Hylite.

I hope it helps!

4 0

4 years ago

A B C D HELP ME OUT PLEASE:))

Andrew [12]

C is your correct answer on this one

3 0

3 years ago

Read 2 more answers

Please provide the step by step explanation. People never do that

777dan777 [17]

Answer:

D) √15

Step-by-step explanation:

An irrational number is a number that can be expressed as an infinite decimal with no set of consecutive digits repeating itself indefinitely and that cannot be expressed as the quotient of two integers.

Therefore the answer would be D) √15 because the decimals keep going

A) 1.52 just ends like so

B) -13³ equals -2197

C) 9/4 equals 2.25

8 0

4 years ago

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Which values best approximate the solutions of –1.5x2 + 4x + 2.2 = 0