Mathematics, 12.08.2020 08:01 dessyrob05

The weight of a small starbucks coffee is a normally distributed random variable with a mean of 325 grams and a standard deviation of 10 grams. Find the weight that corresponds to each event (round your final answers to 2 decimal places)

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Answers

a. Highest 10 percent

b. Middle 50 percent

the weight that corresponds to Highest 10% = 337.8

the weight that corresponds to Middle 50 % lies between 318.26 and 331.74

Step-by-step explanation:

From the information provided for us:

we have the mean = 325

the standard deviation = 10

The objective is to find the weight that corresponds to each event i.e for event (a) , highest 10%

So;

The probability of P (Z > z) = 10%

Same as:

0.1 = 1 - P( Z < z)

P( Z < z) = 1 - 0.1

P( Z < z) = 0.9

From the standard normal tables for z;

P( Z < 1.28) = 0.9

z = 1.28

Similarly. from the z formula; we have:

$z = \dfrac{X - \mu}{\sigma}$

$z \times \sigma = X - \mu$

$z \times \sigma + \mu= X$

$X= z \times \sigma + \mu$

X = (1.28 × 10) + 325

X = 12.8 + 325

X = 337.8

Therefore, the weight that corresponds to Highest 10% = 337.8

b. the weight that corresponds to Middle 50 % can be computed as follows:

the region of z values at 0.50 lies between -0.674 and +0.674

from the z formula; we have:

$z = \dfrac{X - \mu}{\sigma}$

$z \times \sigma = X - \mu$

$z \times \sigma + \mu= X$

$X= z \times \sigma + \mu$

X = -0.674 × 10 + 325 and X = 0.674 × 10 + 325

X = - 6.74 + 325 and X = 6.74 + 325

X = 318.26 and X = 331.74

the weight that corresponds to Middle 50 % lies between 318.26 and 331.74

Answer from: Quest

step-by-step explanation:

Answer from: Quest

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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