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3 years ago

Help with math please

Mathematics

2 answers:

Pavlova-9 [17]3 years ago

6 0

Answer:

C=both a and b

Step-by-step explanation:

Karo-lina-s [1.5K]3 years ago

4 0

Answer:

C. both A and B...............

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4 years ago

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The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 55 o

Usimov [2.4K]

Answer:

a) For this case and using the empirical rule we can find the limits in order to have 9% of the values:

$\mu -2\sigma = 55 -2*6 =43$

$\mu +2\sigma = 55 +2*6 =67$

95% of the widget weights lie between 43 and 67

b) For this case we know that 37 is 3 deviations above the mean and 67 2 deviations above the mean since within 3 deviation we have 99.7% of the data then the % below 37 would be (100-99.7)/2 = 0.15% and the percentage above 67 two deviations above the mean would be (100-95)/2 =2.5% and then we can find the percentage between 37 and 67 like this:

$100 -0.15-2.5 = 97.85$

c) We want to find the percentage above 49 and this value is 1 deviation below the mean so then this percentage would be (100-68)/2 = 16%

Step-by-step explanation:

For this case our random variable of interest for the weights is bell shaped and we know the following parameters.

$\mu = 55, \sigma =6$

We can see the illustration of the curve in the figure attached. We need to remember that from the empirical rule we have 68% of the values within one deviation from the mean, 95% of the data within 2 deviations and 99.7% of the values within 3 deviations from the mean.

Part a

For this case and using the empirical rule we can find the limits in order to have 9% of the values:

$\mu -2\sigma = 55 -2*6 =43$

$\mu +2\sigma = 55 +2*6 =67$

95% of the widget weights lie between 43 and 67

Part b

For this case we know that 37 is 3 deviations above the mean and 67 2 deviations above the mean since within 3 deviation we have 99.7% of the data then the % below 37 would be (100-99.7)/2 = 0.15% and the percentage above 67 two deviations above the mean would be (100-95)/2 =2.5% and then we can find the percentage between 37 and 67 like this:

$100 -0.15-2.5 = 97.85$

Part c

We want to find the percentage above 49 and this value is 1 deviation below the mean so then this percentage would be (100-68)/2 = 16%