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lubasha [3.4K]
3 years ago
10

A food processor packages orange juice in small jars. The weights of the filled jars are approximately normally distributed with

a mean of 10.5 ounces and a standard deviation of 0.3 ounce. Find the proportion of all jars packaged by this process that have weights that fall above 10.983 ounces.
Mathematics
1 answer:
Ratling [72]3 years ago
8 0

Answer:

P(X>10.983)=P(\frac{X-\mu}{\sigma}>\frac{10.983-\mu}{\sigma})=P(Z>\frac{10.983-10.5}{0.3})=P(z>1.61)

And we can find this probability using the complement rule and with excel or the normal standard table:

P(z>1.61)=1-P(z

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 weights of a population, and for this case we know the distribution for X is given by:

X \sim N(10.5,0.3)  

Where \mu=10.5 and \sigma=0.3

We are interested on this probability

P(X>10.983)

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>10.983)=P(\frac{X-\mu}{\sigma}>\frac{10.983-\mu}{\sigma})=P(Z>\frac{10.983-10.5}{0.3})=P(z>1.61)

And we can find this probability using the complement rule and with excel or the normal standard table:

P(z>1.61)=1-P(z

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Step-by-step explanation:

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3 years ago
Determine all values of h and k for which the system S 1 -3x - 3y = h -4x + ky = 10 has no solution. k= ht
Lana71 [14]

Answer:

h\neq 7.5

k = -4

Step-by-step explanation:

Given system of equations are,

-3x-3y = h

-4x + ky = 10

We have to find the values of h and k such that system of equations has no solution.

The standard form of system of equation in two variables can be given by,

a_1x+b_1y+c_1=0

a_2x+b_2y+c_2=0

And condition for the system of equations has no solution is given by,

\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq \dfrac{c_1}{c_2}

So, by comparing the standard form of equations with given equations, the condition such that system has no solution can be written as,

\dfrac{-3}{-4}=\dfrac{-3}{k}\neq \dfrac{h}{10}

=>\dfrac{-3}{-4}=\dfrac{-3}{k}

=> k = -4

and \dfrac{-3}{-4}\neq \dfrac{h}{10}

    =>\ \dfrac{-3\times 10}{-4}\neq h

    =>\ h\neq \dfrac{30}{4}

    =>\ h\neq 7.5

So, the value of h and k for above given system of equations is

h\neq 7.5 and k = -4.

7 0
3 years ago
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