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2 years ago

The formula for the area of a triangle is A = kbh, where A is the area, b is the base

Mathematics

1 answer:

BigorU [14]2 years ago

4 0

Answer:

A / kb = h

Step-by-step explanation:

A = kbh

Divide each side by kb

A / kb = hkb/kb

A / kb = h

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A machine that produces ball bearings has initially been set so that the true average diameter of the bearings it produces is .5

lara [203]

Answer:

7.3% of the bearings produced will not be acceptable

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 0.499, \sigma = 0.002$

Target value of .500 in. A bearing is acceptable if its diameter is within .004 in. of this target value.

So bearing larger than 0.504 in or smaller than 0.496 in are not acceptable.

Larger than 0.504

1 subtracted by the pvalue of Z when X = 0.504.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{0.504 - 0.494}{0.002}$

$Z = 2.5$

$Z = 2.5$ has a pvalue of 0.9938

1 - 0.9938= 0.0062

Smaller than 0.496

pvalue of Z when X = -1.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{0.496 - 0.494}{0.002}$

$Z = -1.5$

$Z = -1.5$ has a pvalue of 0.0668

0.0668 + 0.0062 = 0.073

7.3% of the bearings produced will not be acceptable

4 0

3 years ago

When finding the margin of error for the mean of a normally distributed population from a sample, what is the critical probabili

svlad2 [7]

Critical probability is the essentially cut-off value. The critical probability when the confidence level of 58% is 0.79.

<h3>What is the critical probability?</h3>

Critical probability is the essentially cut-off value that defines the region where the test statistic is unlikely to lie.

As it is given that the confidence level is 58%. therefore, in order to calculate the critical probability, we need to calculate the margin of error within a set of data, and it is given by the formula

$\rm Critical\ Probability, (P*) = 1-\dfrac{\alpha }{2}$