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svp [43]
3 years ago
12

14. (4 points) Alfador produces gear for a racquetball league. It costs him $0.005 per square centimeter to produce racquetballs

for the league. In the past, the league used racquetballs with diameter 4 cm, and he produced 30, 000 racquetballs. However, league regulations now require racquetballs to have diameter 4.05 cm. Use differentials to estimate the increase in cost that Alfador must suffer in order to produce 30, 000 racquetballs under its new regulations. Should this be an overestimate or an underestimate
Mathematics
1 answer:
Rudik [331]3 years ago
6 0

Answer:

i dont know

Step-by-step explanation:

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Answer:

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We are interested on this probability

P(X>140)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

And we can find this probability using the complement rule:

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Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

X \sim N(114.8,13.1)  

Where \mu=114.8 and \sigma=13.1

We are interested on this probability

P(X>140)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:P(X>140)=P(\frac{X-\mu}{\sigma}>\frac{140-\mu}{\sigma})=P(Z>\frac{140- 1114.8}{2.6})=P(z>1.924)And we can find this probability using the complement rule:

P(z>1.924)=1-P(z

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Step-by-step explanation:

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