A box of oatmeal must contain 16 oz. The machine that fills the oatmeal boxes is set so that, on the average, a box contains 16.5 oz. The boxes filled by the machine have weights that can be closely approximated by a normal curve. What fraction of the boxes filled by the machine are underweight if the standard deviation is as follows? 29. 0.5 oz 30. 0.3 oz 31. 0.2 oz 32. 0

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08-05-2020
Mathematics

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A box of oatmeal must contain 16 oz. The machine that fills the oatmeal boxes is set so that, on the average, a box contains 16.5 oz. The boxes filled by the machine have weights that can be closely approximated by a normal curve. What fraction of the boxes filled by the machine are underweight if the standard deviation is as follows? 29. 0.5 oz 30. 0.3 oz 31. 0.2 oz 32. 0

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jmonterrozar jmonterrozar · Answer 1 · 2020-05-12T02:59:02+02:00

Answer:

29. 15.87%

30. 4.75%

31. 0.62%

32. probability cannot be calculated (0%)

Step-by-step explanation:

We have that the formula of the normal distribution is:

z = (x - m) / sd

where x is the value we are going to evaluate, m is the mean and sd is the standard deviation

x = 16 and m = 16.5

when sd = 0.5

z = (16 - 16.5) /0.5

z = -1

Now when looking in the z table, we have that the corresponding value is 0.1587, that is, the probability is 15.87%

when sd = 0.3

z = (16 - 16.5) /0.3

z = -1.67

Now when looking in the z table, we have that the corresponding value is 0.0475, that is, the probability is 4.75%

when sd = 0.2

z = (16 - 16.5) /0.2

z = -2.5

Now when looking in the z table, we have that the corresponding value is 0.0062, that is, the probability is 0.62%

when sd = 0

z = (16 - 16.5) / 0

z = infinity

probability cannot be calculated

keshavgandhi04 keshavgandhi04 · Answer 2 · 2021-11-28T08:15:08+01:00

For standard deviation 0.5 the probability is 15.87%, for standard deviation 0.3 the probability is 4.75%, for standard deviation 0.2 the probability is 0.62%, and for standard deviation 0 the probability cannot be calculated.

Given :

A box of oatmeal must contain 16 oz. The machine that fills the oatmeal boxes is set so that, on average, a box contains 16.5 oz.
The boxes filled by the machine have weights that can be closely approximated by a normal curve.

When the standard deviation is sd = 0.5 . So, the formula of normal distribution becomes:

[tex]z = \dfrac{16-16.5}{0.5} = -1[/tex]

From the z-table, the corresponding value is 0.1587. So, the probability is 15.87%.

When the standard deviation is sd = 0.3 . So, the formula of normal distribution becomes:

[tex]z = \dfrac{16-16.5}{0.3} = -1.67[/tex]

From the z-table, the corresponding value is 0.0475. So, the probability is 4.75%.

When the standard deviation is sd = 0.2 . So, the formula of normal distribution becomes:

[tex]z = \dfrac{16-16.5}{0.2} = -2.5[/tex]

From the z-table, the corresponding value is 0.0062. So, the probability is 0.62%.

When the standard deviation is sd = 0. So, the formula of normal distribution becomes:

[tex]\rm z = \dfrac{16-16.5}{0} = infinity[/tex]

Probability cannot be calculated.

For more information, refer to the link given below:

https://brainly.com/question/21586810