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s344n2d4d5 [400]
3 years ago
5

Suppose Kristen is researching failures in the restaurant business. In the city where she lives, the probability that an indepen

dent restaurant will fail in the first year is 43 % . 43%. She obtains a random sample of 66 independent restaurants that opened in her city more than one year ago and determines if each one had closed within a year. What are the mean and standard deviation of the number of restaurants that failed within a year
Mathematics
1 answer:
FinnZ [79.3K]3 years ago
7 0

Answer:

Mean = 28.38

Standard Deviation = 4.02

Step-by-step explanation:

Probability that a restaurant failed in the first year = p = 43% = 0.43

The probability of occurrence is constant. The events(failing of restaurants) are independent. Number of trials if fixed and there are only two possible outcomes i.e. either restaurant failed or not failed.

This scenario satisfies all the conditions of a Binomial experiment setting. So, we will use Binomial Experiment to answer the questions.

The formula to calculate the Mean of Binomial Distribution is:

Mean = u = np

Here, n is the number of trials, which is 66 in this case. So,

Mean = u = 66 x 0.43 =  28.38

Standard Deviation of a Binomial Distribution is calculated as:

s=\sqrt{np(1-p)} \\\\ s=\sqrt{66 \times 0.43 \times (1-0.43)}\\\\ s=\sqrt{16.1766}\\\\ s=4.02

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3 years ago
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Four lawn sprinkler heads are fed by a 1.9-cm-diameter pipe. The water comes out of the heads at an angle of 35° above the horiz
klemol [59]

Answer:

Step-by-step explanation:

Given:

Angle, θ = 35°

Vertical distance, Δx = 6 m

Diameter, d = 1.9 cm

= 0.019 m

A.

When the water leaves the sprinkler, it does so at a projectile motion.

Therefore,

Using equation of motion,

(t × Vox) = 2Vo²(sin θ × cos θ)/g

= Δx = 2Vo²(sin 35 × cos 35)/g

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= 62.57

Vo = 7.91 m/s

B.

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Diameter, D = 3 × 10^-3 m

As = π × (3 × 10^-3)²/4

= 7.069 × 10^-6 m²

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= area, As × velocity, Vo

= (7.069 × 10^-6) × 7.91

= 5.59 × 10^-5 m³/s

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1 m³ = 1000 liters

= 5.59 × 10^-5 m³/s × 1000 liters/1 m³

= 5.59 × 10^-2 liters/s

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The rate at which volume is flowing in the 4 sprinklers = 4 × 0.0559

= 0.224 liters/s

C.

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= 2.24 × 10^-4 m³/s

Velocity of the water, Vw = volumetric flowrate/area

= 2.24 × 10^-4/2.84 × 10^-4

= 0.787 m/s

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viva [34]

Answer:

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I hope this helps have a great day :)

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