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ExtremeBDS [4]
3 years ago
13

The population of weights of a particular fruit is normally distributed, with a mean of 464 grams and a standard deviation of 6

grams. If 27 fruits are picked at random, then 2% of the time, their mean weight will be greater than how many grams?
Mathematics
1 answer:
igomit [66]3 years ago
7 0

Answer:

If 27 fruits are picked at random, then 2% of the time, their mean weight will be greater than 466.37 grams

Step-by-step explanation:

Mean = \mu = 464

Standard deviation =\sigma = 6

We are supposed to find If 27 fruits are picked at random, then 2% of the time, their mean weight will be greater than how many grams i.e.P(X>x)=0.02

The mean weight is in the highest 2%, you want to go to a z-table and find the z-score that where the area to the left of the curve is closest to 0.98.

n = 27

Refer the z -table

P(Z>x)=2.06

\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}=2.06\\\frac{x-464}{\frac{6}{\sqrt{27}}}=2.06\\x-464=2.06 \times \frac{6}{\sqrt{27}}\\x=(2.06 \times \frac{6}{\sqrt{27}})+464\\x=466.37

So, If 27 fruits are picked at random, then 2% of the time, their mean weight will be greater than 466.37 grams

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Inessa05 [86]

Shown in the graph

<h2>Explanation:</h2>

Using graph tools we can graph the function:

g(x)=4x^2-16

which is the red graph shown below. As you can see, this is a parabola. The rule for vertical and horizontal shifts is as follows:

Let \ c \ be \ a \ positive \ real \ number. \ \mathbf{Vertical \ and \ horizontal \ shifts} \\ in \ the \ graph \ of \ y=f(x) \ are \ represented \ as \ follows:

\bullet \ Vertical \ shift \ c \ units \ \mathbf{upward}: \\ h(x)=f(x)+c \\ \\ \bullet \ Vertical \ shift \ c \ units \ \mathbf{downward}: \\ h(x)=f(x)-c \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ right \ \mathbf{right}: \\ h(x)=f(x-c) \\ \\ \bullet \ Horizontal \ shift \ c \ units \ to \ the \ left \ \mathbf{left}: \\ h(x)=f(x+c)

Therefore, If we shift the red graph 9 units to the right and 1 down, our new function (let's call it h(x)) will be:

h(x)=4\left(x-9\right)^{2}-16-1 \\ \\ Simplifying: \\ \\ h(x)=4\left(x-9\right)^{2}-17

This graph is the blue graph below. Let's verify the transformation taking the vertex of the red graph:

(0,-16)

By translating the 9 units to the right and 1 down the vertex is also translated by the same rule, so:

New \ vertex: \\ \\ (0+9,-16-1) \\ \\ (9,-17)

<h2>Learn more:</h2>

Cubic function: brainly.com/question/13773618#

#LearnWithBrainly

5 0
3 years ago
The present age of father is thrice as old as the age of daughter 5 years ago. If 5 years hence ,the age of father will be twice
pav-90 [236]

Answer:

<em>Hence the daughter's present age is 15 years</em>

<em>The fathers present age is 35 years</em>

<em></em>

Step-by-step explanation:

Let the present age of daughter be x

Let the present age of father be y

5 years ago;

Daughter's age = x - 5

Fathers age = y - 5

If the present age of father is thrice as old as the age of daughter 5 years ago, then;

y - 5 = 3(x-5)

y - 5 = 3x-15

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In 5 years time;

Daughters age = x + 5

Fathers age = y + 5

If the age of father will be twice the age of his daughter in 5 years time then;

y+5 = 2(x+5)

y+5 = 2x + 10

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Equate 1 and 2;

3x - 10 = 2x + 5

3x - 2x = 5 + 10

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Since y = 2x + 5

y = 2(15) + 5

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<em>Hence the daughter's present age is 15 years</em>

<em>The fathers present age is 35 years</em>

<em></em>

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slope is 3x = 3

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