An ordinary (fair) die is a cube with the numbers

A town recently dismissed 9 employees in order to meet their new budget reductions. The town had 7 employees over 50 years of ag

raketka [301]

Answer: 0.1340

Step-by-step explanation:

The binomial distribution formula is given by :-

$P(x)=^nC_xp^x(1-p)^{n-x}$ , where P(x) is the probability of x successes out of n trials, p is the probability of success on a particular trial.

Given : The number of employees over 50 years of age =7

The probability of employees over 50 years of age = $\dfrac{7}{7+15}=0.318$

Number of dismissed employees : n= 9

Now, the required probability will be :

$P(x =1)=^{9}C_1(0.318)^{1}(1-0.318)^{9-1}\\\\=(9)(0.318)(1-0.318)^{8}=0.133950588714\approx0.1340$

Thus, the probability that exactly 1 employee was over 50 = 0.1340

3 0

3 years ago

ABC is a tangent to the circle below. O is the centre of the circle. Work out the size of angle 0. Give reasoning to justify you

Delvig [45]

Answer:

Θ = 46°

Step-by-step explanation:

the angle between a tangent and a radius at the point of contact is 90° , so

∠ ABO = 90°

since OB = OD ( radii of circle ) then Δ BOD is isosceles and

∠ OBD = ∠ ODB = 22°

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ AOB is an exterior angle of the triangle , then

∠ AOB = 22° + 22° = 44°

the sum of the 3 angles in Δ AOB = 180° , then

Θ + 44° + 90° = 180°

Θ + 134° = 180° ( subtract 134° from both sides )

Θ = 46°

6 0

1 year ago

Suppose that the mean water hardness of lakes in Kansas is 425 mg/L and these values tend to follow a normal distribution. A lim

tino4ka555 [31]

Answer:

The mean water hardness of lakes in Kansas is 425 mg/L or greater.

Step-by-step explanation:

We are given the following data set:

346, 496, 352, 378, 315, 420, 485, 446, 479, 422, 494, 289, 436, 516, 615, 491, 360, 385, 500, 558, 381, 303, 434, 562, 496

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{10959}{25} =438.36$

Sum of squares of differences = 175413.76

$S.D = \sqrt{\dfrac{175413.76}{24}} = 85.49$

Population mean, μ = 425 mg/L

Sample mean, $\bar{x}$ = 438.36

Sample size, n = 25

Alpha, α = 0.05

Sample standard deviation, s = 85.49

First, we design the null and the alternate hypothesis

$H_{0}: \mu \geq 425\text{ mg per Litre}\\H_A: \mu < 425\text{ mg per Litre}$

We use one-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{438.36 - 425}{\frac{85.49}{\sqrt{25}} } = 0.7813$

Now, $t_{critical} \text{ at 0.05 level of significance, 24 degree of freedom } = -1.7108$

Since,

The calculated t-statistic is greater than the critical value, we fail to reject the null hypothesis and accept it.

Thus, the mean water hardness of lakes in Kansas is 425 mg/L or greater.

6 0

3 years ago

How many sides in the decagon

rosijanka [135]

Answer:

10

Step-by-step explanation:

pls mark me as brainliest :))

6 0

3 years ago

Read 2 more answers

Using the Empirical Rule, it is found that:

AveGali [126]

Considering that the mean of the normal distribution is the same as the median, the median is of 88%.

<h3>What does the Empirical Rule state?</h3>

It states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

For the normal distribution, the median is the same of the mean, that is, the median is of 88%.

More can be learned about the Empirical Rule and the normal distribution at brainly.com/question/24537145

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8 0

2 years ago