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Sergio [31]
3 years ago
10

Emails arrive at the server of a company at the rate of an average of 10 per hour. It is assumed that a Poisson process is a goo

d model for the arrivals of the emails. What is the probability (to 2 decimal places) that the time between two consecutive emails is more than two minutes?
Mathematics
1 answer:
fomenos3 years ago
4 0

Answer:

0.37

Step-by-step explanation:

we have given that emails arrives at the server at the rate of 10 per hour means \frac{10}{60}=0.166  per minute

we have to find the probability that the time difference between the two email is more than 2 minute

so probability P\left ( X> 2 \right )=e^{-2\lambda }=e^{-2\times 0.166}=0.7166

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Simplify a2b3×a5b2​
Kryger [21]

Answer:

\huge \orange { {a}^{7}  {b}^{5} }

Step-by-step explanation:

\huge {a}^{2}  {b}^{3}  \times  {a}^{5}  {b}^{2}  \\  \\\huge =  {a}^{2}  \times  {a}^{5}   \times {b}^{3}  \times  {b}^{2}  \\ \\\huge =  {a}^{2 + 5}  \times  {b}^{3 + 2}  \\ \\  \huge \red{=  {a}^{7}  {b}^{5} }

6 0
3 years ago
A synthetic fiber used in manufacturing carpet has tensile strength that is normally distributed with mean 75.5 psi and standard
Sedaia [141]

Answer:

The standard deviation reduces when sample size (n) increases

Step-by-step explanation:

From the above information given, we have that mean = 75.5

Standard deviation = 3.5

But Standard deviation = √summation (x-u)/n

This simply implies that when sample (n) is increased there would be a reduction in the standard deviate.

7 0
2 years ago
14.12 = 1/2 (3.6x - 12.8)<br><br> show work
Sergio039 [100]

Answer:

x = 11.4

Step-by-step explanation:

14.12 = \frac{1}{2} ( 3.6x - 12.8 )

Rewrite so that the equation is entirely in decimals;

14.12 = 0.5( 3.6x - 12.8 )

Distribute;

14.12 = 1.8x - 6.4

Inverse operations;

14.12 = 1.8x - 6.4

+6.4            +6.4

20.52 = 1.8x

/1.8        /1.8

11.4 = x

4 0
3 years ago
Read 2 more answers
Navy PilotsThe US Navy requires that fighter pilots have heights between 62 inches and78 inches.(a) Find the percentage of women
Zigmanuir [339]

The first part of the question is missing and it says;

Use these parameters: Men's heights are normally distributed with mean 68.6 in. and standard deviation 2.8 in. Women's heights are normally distributed with mean 63.7 in. and standard deviation 2.9 in.

Answer:

A) Percentage of women meeting the height requirement = 72.24%

B) Percentage of men meeting the height requirement = 0.875%

C) Corresponding women's height =67.42 inches while corresponding men's height = 72.19 inches

Step-by-step explanation:

From the question,

For men;

Mean μ = 68.6 in

Standard deviation σ = 2.8 in

For women;

Mean μ = 63.7 in

Standard deviation σ = 2.9 in

Now let's calculate the standardized scores;

The formula is z = (x - μ)/σ

A) For women;

Z = (62 - 63.7)/2.9 = - 0.59

Z = (78 - 63.7)/2.9 = 4.93

The original question cam be framed as;

P(62 < X < 78).

So thus, the probability of only women will take the form of;

P(-0.59 < Z < 4.93) = P(Z<4.93) - P(Z > - 0.59)

From the normal probability table attached, when we interpolate, we'll arrive at P(Z<4.93) = 0.9999996

And P(Z > - 0.59) = 0.277595

Thus;

P(Z<4.93) - P(Z > - 0.59) =0.9999996 - 0.277595 = 0.7224

So, percentage of women meeting the height requirement is 72.24%.

B) For men;

Z = (62 - 68.6)/2.8 = -2.36

Z = (78 - 68.6)/2.8 = 3.36

Thus, the probability of only men will take the form of;

P(-2.36 < Z < 3.36) = P(Z<3.36) - P(Z > - 2.36)

From the normal probability table attached, when we interpolate, we'll arrive at P(Z<3.36) = 0.99961

And P(Z > -2.36) = 0.99086

Thus;

P(Z<3.36) - P(Z > -2.36) 0.99961 - 0.99086 = 0.00875

So, percentage of women meeting the height requirement is 72.24%.

B)For women;

Z = (62 - 63.7)/2.9 = - 0.59

Z = (78 - 63.7)/2.9 = 4.93

The original question cam be framed as;

P(62 < X < 78).

So thus, the probability of only women will take the form of;

P(-0.59 < Z < 4.93) = P(Z<4.93) - P(Z > - 0.59)

From the normal probability table attached, when we interpolate, we'll arrive at P(Z<4.93) = 0.9999996

And P(Z > - 0.59) = 0.277595

Thus;

P(Z<4.93) - P(Z > - 0.59) =0.9999996 - 0.277595 = 0.00875

So, percentage of women meeting the height requirement is 0.875%

C) Since the height requirements are changed to exclude the tallest 10% of men and the shortest10% of women.

For women;

Let's find the z-value with a right-tail of 10%. From the second table i attached ;

invNorm(0.90) = 1.2816

Thus, the corresponding women's height:: x = (1.2816 x 2.9) + 63.7= 67.42 inches

For men;

We have seen that,

invNorm(0.90) = 1.2816

Thus ;

Thus, the corresponding men's height:: x = (1.2816 x 2.8) + 68.6 = 72.19 inches

7 0
3 years ago
You buy milk in 1 gallon containers. One portion of waffles requires 0.4 ounces of milk. How many portions can be made with one
xenn [34]

320 portions of waffles can be made with one container.

Step-by-step explanation:

Given,

Milk is bought in 1 gallon container.

One portion of waffles require = 0.4 ounces of milk

We know that;

1 gallon = 128 ounces

Now;

No. of portions of waffles = \frac{Total\ ounces\ of\ milk}{Milk\ used\ per\ waffle}

No. of portions of waffles = \frac{128}{0.4}

No. of portions of waffles = 320

320 portions of waffles can be made with one container.

5 0
3 years ago
Read 2 more answers
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