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Leokris [45]
3 years ago
14

Delicious Candy markets a two-pound box of assorted chocolates. Because of imperfec- tions in the candy making equipment, the ac

tual weight of the chocolate has a uniform distribution ranging from 31 to 32.5 ounces. What is the probability that a box weighs less than 31.8 ounces?
Mathematics
1 answer:
saveliy_v [14]3 years ago
6 0

Answer:

The required probability is 0.533.

Step-by-step explanation:

Consider the provided information.

The actual weight of the chocolate has a uniform distribution ranging from 31 to 32.5 ounces.

Let x is the random variable for the actual weight of chocolate.

According to PDF function.

P(a\leq x\leq b)=\int\limits^b_a {f(x)} \, dx

Where f(x)=\left\{\begin{matrix}\frac{1}{b-a} & a

It is given that ranging from 31 to 32.5 ounces.

Substitute a=31 and b=32.5 in above function.

f(x)=\left\{\begin{matrix}\frac{1}{32.5-31} & 31

f(x)=\left\{\begin{matrix}\frac{1}{1.5} & 31

We need to find the probability that a box weighs less than 31.8 ounces

Now according to PDF:

P(x

P(x

Hence, the required probability is 0.533.

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If p varies directly with q, and p = 10 when q = 5, what is the value of p when q = 20
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Jessica can walk 2 1/2 miles in 3/4 of an hour. What is her speed in miles per<br> hour?
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3 1/3 miles

Step-by-step explanation:

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A camp needs 100 students to help with 4-year-old campers. Eight students from 4 different classes have agreed to help. How many
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3 years ago
A manager wishes to determine the relationship between the number of miles (in hundreds of miles) the manager's sales representa
Aleksandr [31]

Answer:

y=3.529 x +37.91

We can predict the sales representative travelled 8 miles replacing x =8 and we got:

y(8) = 3.529*8 + 37.91= 66.142

And we can predict the sales representative travelled 11 miles replacing x =11 and we got:

y(11) = 3.529*11 + 37.91= 76.729

Step-by-step explanation:

For this case we have the following data:

Miles Traveled x: 2,3,10,7,8,15,3,1,11

Sales y :31,33,78,62,65,61,48,55,120

For this case we need to calculate the slope with the following formula:

m=\frac{S_{xy}}{S_{xx}}

Where:

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}

So we can find the sums like this:

\sum_{i=1}^n x_i =60

\sum_{i=1}^n y_i =553

\sum_{i=1}^n x^2_i =582

\sum_{i=1}^n y^2_i =39653

\sum_{i=1}^n x_i y_i =4329

With these we can find the sums:

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=582-\frac{60^2}{9}=182

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=4329-\frac{60*553}{9}=642.33

And the slope would be:

m=\frac{642.33}{182}=3.529

Nowe we can find the means for x and y like this:

\bar x= \frac{\sum x_i}{n}=\frac{60}{9}=6.67

\bar y= \frac{\sum y_i}{n}=\frac{553}{9}=61.44

And we can find the intercept using this:

b=\bar y -m \bar x=61.44-(3.529*6.67)=37.91

So the line would be given by:

y=3.529 x +37.91

We can predict the sales representative travelled 8 miles replacing x =8 and we got:

y(8) = 3.529*8 + 37.91= 66.142

And we can predict the sales representative travelled 11 miles replacing x =11 and we got:

y(11) = 3.529*11 + 37.91= 76.729

4 0
3 years ago
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