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jeka94
3 years ago
15

Before every​ flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the ai

rcraft. The aircraft can carry 41 ​passengers, and a flight has fuel and baggage that allows for a total passenger load of 6 comma 683 lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than StartFraction 6 comma 683 l b Over 41 EndFraction equals 163 lb. What is the probability that the aircraft is​ overloaded? Should the pilot take any action to correct for an overloaded​ aircraft? Assume that weights of men are normally distributed with a mean of 180.5 lb and a standard deviation of 38.2.
Mathematics
1 answer:
ss7ja [257]3 years ago
7 0

Answer:

The probability that the plane is oveloaded is P=0.9983.

The pilot should take out the baggage and send it in another plain or have less passengers in the plain to not overload.

Step-by-step explanation:

The aircraft will be overloaded if the mean weight of the passengers is greater than 163 lb.

If the plane is full, we have 41 men in the plane. This is our sample size.

The weights of men are normally distributed with a mean of 180.5 lb and a standard deviation of 38.2.

So the mean of the sample is 180.5 lb (equal to the population mean).

The standard deviation is:

\sigma=\frac{\sigma}{\sqrt{N}} =\frac{38.2}{\sqrt{41}}=\frac{38.2}{6.4} =5.97

Then, we can calculate the z value for x=163 lb.

z=\frac{x-\mu}{\sigma}=\frac{163-180.5}{5.97}=\frac{-17.5}{5.97}=   -2.93

The probability that the mean weight of the men in the airplane is below 163 lb is P=0.0017

P(\bar X

Then the probability that the plane is oveloaded is P=0.9983:

P(overloaded)=1-P(X

The pilot should take out the baggage or have less passengers in the plain to not overload.

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You invested $7,000 into a money market account for 10 years at an annual interest rate of 3%. How much is the accrued interest?
steposvetlana [31]

The total interest accrued is $2,407.41 if you invested $7,000 into a money market account for 10 years at an annual interest rate of 3%.

<h3>What is invested amount?</h3>

An investment is a payment made to acquire the securities of other firms with the intention of making a profit.

We are assuming the interest will be compounded annually

\rm A = P(1+\dfrac{r}{n})^{nt}

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

We have:

P = $7000

r = 3% = 0.03

t = 10 years

n = 1

\rm A = 7000(1+\dfrac{0.03}{1})^{1\times10}

After calculating:

A = $9407.41

I = A - P = 9407.41 - 7000 = $2,407.41

Thus, the total interest accrued is $2,407.41 if you invested $7,000 into a money market account for 10 years at an annual interest rate of 3%.

Learn more about the invested amount here:

brainly.com/question/16995381

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4 0
2 years ago
Mr. Gonzalez built two identical flower beds in his yard with the dimensions shown. A prism has a length of 6 feet, height of 2
Lady bird [3.3K]

Answer:

For the 2 the identical flower beds he will require 44 × 2 = 88 ft² of paints to paint the sides of the beds.

Step-by-step explanation:

The prisms are 2 identical flower beds . The dimensions are the same which have a length of 6 ft , height of 2 ft and width of 5 ft. He wants to paints the side of the beds which is the lateral area of the prisms.

Lateral surface area of a rectangular prism is adding the area of the lateral faces of the prism.

Lateral surface area = PH

P = perimeter of the side

H = height

perimeter = (2L + 2W)

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L = length

W = width

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W = 5 ft

perimeter = (2L + 2W)

perimeter = (2 × 6 + 2 × 5)

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Lateral area = 22 × 2

Lateral area = 44 ft²

For the 2 the identical flower beds he will require 44 × 2 = 88 ft² of paints to paint the sides of the beds.

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3 years ago
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GREYUIT [131]
The second one

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4 0
3 years ago
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A computer cost £900. It is on sale for 25% off. You also need to pay 6% sales tax. What is the final price of the computer?
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