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oksano4ka [1.4K]
2 years ago
6

normally distributed with mean 24.6 seconds and standard deviation 0.64 seconds;the lower finishing time, the better. If the qua

lifying time for this event for the regionalchampionship is set so that the top 15 percent of all runners qualify, then thatqualifying time in seconds is about
Mathematics
1 answer:
marshall27 [118]2 years ago
3 0

Answer:

z=1.04

And if we solve for a we got

a=24.6 +1.04*0.64=25.27

So the value of height that separates the bottom 85% of data from the top 15% is 25.27.  

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the finishing time of a population, and for this case we know the distribution for X is given by:

X \sim N(24.6,0.64)  

Where \mu=24.6 and \sigma=0.64

Solution to the problem

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.15   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.85 of the area on the left and 0.15 of the area on the right it's z=1.04. On this case P(Z<1.04)=0.85 and P(z>1.04)=0.15

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=1.04

And if we solve for a we got

a=24.6 +1.04*0.64=25.27

So the value of height that separates the bottom 85% of data from the top 15% is 25.27.  

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In the adjoining figure, XY = XZ . YQ and ZP are the bisectors of <img src="https://tex.z-dn.net/?f=%20%5Cangle" id="TexFormula1
svetlana [45]

Answer:

See Below.

Step-by-step explanation:

Statements:                                              Reasons:

1)\, XY=XZ                                              Given

2) \text{ $ m\angle Y= m\angle Z$}                                        Isosceles Triangle Theorem

\displaystyle 3) \text{ $m\angle Y=m\angle XYQ + \angle QYZ$}                  Angle Addition

\displaystyle 4)\text{ $YQ$ bisects $\angle XYZ$}                               Given

5) \text{ $m\angle XYQ=m\angle QYZ$}                           Definition of Bisector

\displaystyle 6)\text{ $m\angle Y=2m\angle QYZ$}                               Substitution

7)\text{ $m\angle Z=m\angle XZP+m\angle PZY$}              Angle Addition

8)\text{ $ZP$ bisects $\angle XZY$}                              Given

\displaystyle 9) \text{ $m\angle XZP=m\angle PZY$ }                          Definition of Bisector

\displaystyle 10) \text{ $ m\angle Z = 2m\angle PZY $}                            Substitution

11)\text{ } 2m\angle QYZ=2m\angle PZY                    Substitution

12)\text{ }m\angle QYZ=m\angle PZY                        Division Property of Equality

13)\text{ } YZ=YZ                                         Reflexive Property

14)\text{ } \Delta YZP\cong\Delta ZYQ                             Angle-Side-Angle Congruence*

15)\text{ } YQ=ZP                                         CPCTC

*For clarification:

∠Y = ∠Z

YZ = YZ (or ZY)

∠PZY = ∠QYZ

So, Angle-Side-Angle Congruence:

ΔYZP is congruent to ΔZYQ

5 0
3 years ago
Read 2 more answers
According to the National Bridge Inspection Standard (NBIS), public bridges over 20 feet in length must be inspected and rated e
slamgirl [31]

Answer:

1.80% probability that in a random sample of 12 major Denver bridges, at least 4 will have an inspection rating of 4 or below in 2020.

Step-by-step explanation:

For each bridge, there are only two possible outcomes. Either it has rating of 4 or below, or it does not. The probability of a bridge being rated 4 or below is independent from other bridges. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

For the year 2020, the engineers forecast that 9% of all major Denver bridges will have ratings of 4 or below.

This means that p = 0.09

Use the forecast to find the probability that in a random sample of 12 major Denver bridges, at least 4 will have an inspection rating of 4 or below in 2020.

Either less than 4 have a rating of 4 or below, or at least 4 does. The sum of the probabilities of these events is 1.

So

P(X < 4) + P(X \geq 4) = 1

We want P(X \geq 4)

So

P(X \geq 4) = 1 - P(X < 4)

In which

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{12,0}.(0.09)^{0}.(0.91)^{12} = 0.3225

P(X = 1) = C_{12,1}.(0.09)^{1}.(0.91)^{11} = 0.3827

P(X = 2) = C_{12,2}.(0.09)^{2}.(0.91)^{10} = 0.2082

P(X = 3) = C_{12,3}.(0.09)^{3}.(0.91)^{9} = 0.0686

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.3225 + 0.3827 + 0.2082 + 0.0686 = 0.982

Finally

P(X \geq 4) = 1 - P(X < 4) = 1 - 0.982 = 0.0180

1.80% probability that in a random sample of 12 major Denver bridges, at least 4 will have an inspection rating of 4 or below in 2020.

6 0
2 years ago
The volume of a 10 ounce box of cheerios is 258.75in3. the length of the box is 4 inches less than the height and the width is 3
Marina86 [1]

Answer:

Height of the box = 11.5 in

Step-by-step explanation:

Let h be the height of the box.

Assuming the volume of the Box is 258.75\ in^3.

Given:

Length = Height - 4 = h - 4

Width = 3 in

We need to find the height of the box.

Solution:

We know that the volume of the box.

Volume = Length\times height\times width

Substitute all given value in above formula.

258.75 = (h-4)\times h\times 3

Rewrite the equation as:

258.75 = 3h(h-4)

258.75 = 3h^2-12h

3h^2-12h-258.75=0

whole equation divided by 3.

h^2-4h-86.25=0

Use quadratic formula with a = 1, b = -4,c=-86.25

h=\frac{-b\pm \sqrt{(b)^{2}-4ac}}{2a}

Put these a, b and c value in above equation.

h=\frac{-(-4)\pm \sqrt{(-4)^{2}-4(1)(-86.25)}}{2(1)}

h=\frac{4\pm \sqrt{16+345}}{2}

h=\frac{4\pm \sqrt{361}}{2}

h=\frac{4\pm 19}{2}

For positive sign

h=\frac{23}{2}  

h = 11.5 in

For negative sign

h=\frac{-15}{2}

h = -7.5

We take positive value of h.

Therefore, the height of the box h = 11.5 in

4 0
2 years ago
45.50 is 30% of what number
m_a_m_a [10]

Answer:

31.85

Step-by-step explanation:

to subtract 30 percent from 45.50 just divide the percentage (30) by 100 subtract this value form 1 then multiply it by the initial value (45.50) so

final value = 45.50 x ( 1 - \frac{30}{100} )

final value = 45.50 x ( 1 - 0.3)

final value = 45.50 x (0.7)

final value = 31.85  

subtract 30% is the same as discount 30% this operation could be for example a 30% discount on 45.50

note: 0.3 can be found just by moving the decimal point 2 places to the left \frac{30}{100} = 0.3 as a decimal

3 0
2 years ago
Example
saul85 [17]

Answer:

EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

6 0
2 years ago
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