Question

Help with this one!!! Show steps pls :)

Sergeeva-Olga [200]

$96\dfrac{11}{20}= 96.55$

96.55%=0.9655

$95.5845:0.9655=99$

Answer: 99

5 0

3 years ago

Read 2 more answers

The CEO of a large manufacturing company is curious if there is a difference in productivity level of her warehouse employees ba

blsea [12.9K]

Answer:

The test statistic is z = -2.11.

Step-by-step explanation:

Before finding the test statistic, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Group 1: Sample of 35, mean of 1276, standard deviation of 347.

This means that:

$\mu_1 = 1276, s_1 = \frac{347}{\sqrt{35}} = 58.6537$

Group 2: Sample of 35, mean of 1439, standard deviation of 298.

This means that:

$\mu_2 = 1439, s_2 = \frac{298}{\sqrt{35}} = 50.3712$

Test if there is a difference in productivity level.

At the null hypothesis, we test that there is no difference, that is, the subtraction is 0. So

$H_0: \mu_1 - \mu_2 = 0$

At the alternate hypothesis, we test that there is difference, that is, the subtraction is different of 0. So

$H_1: \mu_1 - \mu_2 \neq 0$

The test statistic is:

$z = \frac{X - \mu}{s}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis and s is the standard error.

0 is tested at the null hypothesis:

This means that $\mu = 0$

From the two samples:

$X = \mu_1 - \mu_2 = 1276 - 1439 = -163$

$s = \sqrt{s_1^2+s_2^2} = \sqrt{58.6537^2+50.3712^2} = 77.3144$

Test statistic:

$z = \frac{X - \mu}{s}$

$z = \frac{-163 - 0}{77.3144}$

$z = -2.11$

The test statistic is z = -2.11.

7 0

3 years ago

Use the definition of continuity to determine whether f is continuous at a. f(x) = 5x+5 a = -5 Question

Andrej [43]

ANSWER

$lim_{x \to - 5}(f(x)) = f( - 5)$

EXPLANATION

If f(x) is continuous at

$x = a$

Then,

$lim_{x \to a}(f(x)) = f(a)$

The given function is

$f(x) = 5x + 5$

$f( - 5) = 5( - 5) + 5$

$f( - 5) = - 25 + 5 = - 20$

$lim_{x \to - 5}(f(x)) = 5( - 5) + 5$

$lim_{x \to - 5}(f(x)) = - 20$

Since,

$lim_{x \to - 5}(f(x)) = f( - 5)$

The function is continuous at

$x = - 5$

4 0

3 years ago

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A flower vendor sells roses for 50 cents each. how much does she pay per flower if she makes $6.00 on every $20 worth sold

kkurt [141]

We are given

selling price of one flower is $0.50

so, $SP=0.50$

Let's assume

she sold 'n' flowers to get $20

so, total amount she get after selling 'n' flowers is

$=0.50*n$

$=0.50n$

This is supposed to be $20

so, we can set it equal to 20

$20=0.50n$

now, we can solve for n

we get

$n=40$

we are given

she makes $6.00 on every $20 worth sold

so, we can find cost of 40 flowers is 20-6

total cost is 14

or cost of 40 flowers is $14

now, we can find cost of one flower

$CP=\frac{14}{40}$

$CP=0.35$

so, cost of each flower is 35 cents...............Answer

8 0

3 years ago

Find the average value of the function f(x, y, z) = 5x2z 5y2z over the region enclosed by the paraboloid z = 9 − x2 − y2 and the

Katyanochek1 [597]

The paraboloid meets the x-y plane when x²+y²=9. A circle of radius 3, centre origin.

Use cylindrical coordinates (r,θ,z) so paraboloid becomes z = 9−r² and f = 5r²z. 

If F is the mean of f over the region R then F ∫ (R)dV = ∫ (R)fdV 

∫ (R)dV = ∫∫∫ [θ=0,2π, r=0,3, z=0,9−r²] rdrdθdz 

= ∫∫ [θ=0,2π, r=0,3] r(9−r²)drdθ = ∫ [θ=0,2π] { (9/2)3² − (1/4)3⁴} dθ = 81π/2 

∫ (R)fdV = ∫∫∫ [θ=0,2π, r=0,3, z=0,9−r²] 5r²z.rdrdθdz 

= 5∫∫ [θ=0,2π, r=0,3] ½r³{ (9−r²)² − 0 } drdθ 

= (5/2)∫∫ [θ=0,2π, r=0,3] { 81r³ − 18r⁵ + r⁷} drdθ 

= (5/2)∫ [θ=0,2π] { (81/4)3⁴− (3)3⁶+ (1/8)3⁸} dθ = 10935π/8 

∴ F = 10935π/8 ÷ 81π/2 = 135/4

4 0

3 years ago