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14 days ago

5

A grocery store receives deliveries of corn from two farms, one in Iowa and the other in Ohio. Both farms produce ears of corn w

ith mean weight 1.26 pounds. The standard deviation of the weights of the ears of corn from the farm in Ohio is 0.01 pound greater than that from the farm in Iowa. A randomly selected ear of corn from the farm in Iowa weighed 1.39 pounds, which has a standardized score of 1.645 for the distribution of weights for the Iowa corn. If an ear of corn from the farm in Ohio weighs 1.39 pounds, how many standard deviations from the mean is the weight with respect to the Ohio distribution

1 answer:

Zina [3.9K]14 days ago

4 0

Answer:

The number of standard deviations above the mean is $z_o = 1.4607$

Step-by-step explanation:

The question indicates that:

The average weight of the corn ears from each farm is $\mu=1.26$

The standard deviation for the corn ears from Iowa is $\sigma_1$

The standard deviation for the corn ears from Ohio is

$\sigma_2= 0.01 + \sigma_1$

A randomly chosen ear of corn from Iowa weighs x = 1.39 pounds

The standardized score is z = 1.645

The weight of a randomly chosen ear of corn from Ohio measures $x_1 = 1.39\ pound$

In general, the standardized score of corn weight from Iowa can be mathematically defined as:

$z = \frac{ 1.39 - 1.26 }{\sigma_1 }$

=> $1.645 = \frac{ 1.39 - 1.26 }{\sigma_1 }$

=> $\sigma_1 = \frac{ 1.39 - 1.26 }{ 1.64 5}$

=> $\sigma_1 = 0.0790$

Conversely, the standardized score of corn weight from Ohio is expressed as:

$z_o = \frac{ 1.39 - 1.26 }{\sigma_2 }$

=> $z_o= \frac{ 1.39 - 1.26 }{0.01 + \sigma_1 }$

=> $z_o = \frac{ 1.39 - 1.26 }{ 0.089}$

=> $z_o = 1.4607$

A positive value indicates this quantity represents the number of standard deviations above the mean.

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Step-by-step explanation:

Given

The distance from Paris to Los Angeles $d=5000 miles$

Wind traveling at 100 mph from Los Angeles to Paris

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Relative velocity of Plane A is $v_a=550-100 =450 mph$ since Plane A is heading against the wind

Relative velocity of Plane B is $v_b=550+100=650 mph$

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What is the domain of the square root function graphed below ?

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The graph indicates that x never goes below 0. This means the point (-1,0) is not included in the graph. Therefore, D is the only valid option.

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6 days ago

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At a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately no

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Answer:

The correct answer is;

A. 0.17

Step-by-step explanation:

Here are the provided details;

The average time taken for a cashier to handle an order, μ = 276 seconds

The deviation from the average, σ = 38 seconds

The z-score for an order processing time of x = 240 seconds can be calculated as follows;

$Z=\dfrac{x-\mu }{\sigma }$

Thus;

$Z=\dfrac{240-276 }{38 } \approx -0.9474$

The resulting probability

P(z = -0.9474) = 0.17361

Hence, the estimated proportion of orders processed in under 240 seconds is roughly 0.17361 or 0.17 when rounded to two decimal places.

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15 days ago

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Answer: The most significant angle created during his journey appears at the mall, between his house and the library.

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Hi, since this scenario forms a right triangle (refer to the attached image), the angle between his house and the library measures 90°.

For a right triangle, the total of its internal angles equals 180°, making the right angle (90°) the largest among them.

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The line width of a tool used for semiconductor manufacturing is assumed to be normally distributed with a mean of 0.5 micromete

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b. 71.11%

c. 0.564 micrometer

Step-by-step explanation:

To find the z value for each measurement, we must calculate and determine the percentage they correspond to, and the difference will give us the percentage between those two statistics.

The equation for z is:

z = (x - m) / (sd)

Here, x is the value being evaluated, m denotes the mean, and sd represents the standard deviation.

a.

For 0.62 copies, we calculate:

z = (0.62 - 0.5) / (0.05)

z = 2.4

This translates to 0.9918.

Therefore, p (x > 0.62) = 1 - 0.9918

p (x > 0.62) = 0.0082 = 0.82%

b.

For 0.47 copies, we have:

z = (0.47 - 0.5) / (0.05)

z = -0.6, which equates to 0.2742.

For 0.63 copies:

z = (0.63 - 0.5) / (0.05)

z = -2.6, which yields 0.9953.

Hence, p (0.47 > x > 0.63) = 0.9953 - 0.2742

p (0.47 > x > 0.63) = 0.7211 = 72.11 %

c.

For x copies, we find:

p = 0.9 corresponds to z = 1.28.

Thus, 1.28 = (x - 0.5) / (0.05)

From which we derive:

x = 1.28*0.05 + 0.5

x = 0.564 micrometer

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