An employer has a staff of eighty actuaries, ten of whom are student actuaries. A student actuary is allowed a total of ten weeks off per year (52 weeks in a year) for studying, vacation, and sick days. A non-student actuary is given four weeks off a year. It is assumed that all actuaries use all of the weeks off allocated to them. The actuary Mr. Taylor is at work today. What is the probability that he is a student?

Answers

Answer 1

Answer:

0.1111

Step-by-step explanation:

From the given information;

Number of staffs in the actuary = 80

Out of the 80, 10 are students.

i.e.

P(student actuary) = 10/80 = 0.125

number of weeks in a year = 52

off time per year = 10/52 = 0.1923

P(at work || student actuary) = (50 -10/52)

= 42/52

= 0.8077

P(non student actuary) = (80 -10)/80

= 70 / 80

= 0.875

For a non-student, they are only eligible to 4 weeks off in a year

i.e.

P(at work | non student) = (52-4)/52

= 48/52

= 0.9231

P(at work) = P(student actuary) × P(at work || student actuary) + P(non student actuary) × P(at work || non studnet actuary)

P(at work) =  (0.125 × 0.8077) + ( 0.875 × 0.9231)

P(at work) = 0.1009625 + 0.8077125

P(at work) = 0.90868

Finally, the P(he is a student) = (P(student actuary) × P(at work || student actuary) ) ÷ P(at work)

P(he is a student) = (0.125 × 0.8077) ÷ 0.90868

P(he is a student) = 0.1009625 ÷ 0.90868

P(he is a student) = 0.1111


Related Questions

The cost, in dollars, of a gym membership for n months can be described by the explicit equation Pn = 70 + 301. What does this equation tell us?​

Answers

Answer:

70 + 301 = 371

Step-by-step explanation:

This equation tells the gym

why museums are regarded as information resources?​

Answers

Step-by-step explanation:

everything can be found in the picture

Answer:

Hello There!!

Step-by-step explanation:

Museums are regarded as information resources because there are historical things and artifacts there.

hope this helps,have a great day!!

~Pinky~

A band played an encore at 2 of its last 4 shows. Considering this data, how many of the
band's next 14 shows would you expect to have an encore?
shows

Answers

The answer is 7 hope this helps

The number of times that the band played an encore at 7 out of the next 14 shows.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The band should do an encore at a rate of 2 out of every 4 gigs, or 2/4 = 1/2 shows, according to the available statistics.

We may use the following percentage to determine how many of the following 14 performances will likely have an encore:

1/2 = x/14

14 = 2x

x = 7

Therefore, we can expect the band to play an encore at 7 out of the next 14 shows.

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Pls Help I will give Brainliest!

Answers

Answer:

Step-by-step explanation:

2 sin x cos x – sin x = 0

Answers

Answer: PiN, Pi/3+2PiN, 5Pi/3+2PiN

Step-by-step explanation: Use formula sheet

10 mugs and 2 plates cost £54
8 mugs and 2 plates cost £46
Write down and solve simultaneous equations

(M is the cost of a mug and p is the cost of a plate, in £

Answers

Answer:

mug = 4

plate = 7

Step-by-step explanation:

10 x + 2y =54

8x + 2y = 46

2x = 8

x = 4

2y = 14

y = 7

Yam
190
Groundnuts
90
Vegetables
30. What is the ratio of the land used
for groundnuts to the land for
vegetables

Answers

Answer:

3:1

Step-by-step explanation:

90:30 simplified is 3:1

Set up an equation and find the missing value of x.

Answers

Answer:

x = 35

Step-by-step explanation:

The angles shown are vertical angles

Vertical angles are congruent

Hence, 80 = 2x + 10

( Note that we just created an equation that we can use to solve for x )

We now solve for x using the equation we created

80 = 2x + 10

Step 1 subtract 10 from each side

80 - 10 = 70

10 - 10 cancels out

We now have 70 = 2x

Step 2 divide each side by 2

70/2 = 35

2x / 2 = x

We're left with x = 35

Calls to a customer service center last on average 2.8 minutes with a standard deviation of 1.4 minutes. An operator in the call center is required to answer 75 calls each day. Assume the call times are independent. What is the expected total amount of time in minutes the operator will spend on the calls each day

Answers

Answer:

The expected total amount of time the operator will spend on the calls each day is of 210 minutes.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

n-values of normal variable:

Suppose we have n values from a normally distributed variable. The mean of the sum of all the instances is [tex]M = n\mu[/tex] and the standard deviation is [tex]s = \sigma\sqrt{n}[/tex]

Calls to a customer service center last on average 2.8 minutes.

This means that [tex]\mu = 2.8[/tex]

75 calls each day.

This means that [tex]n = 75[/tex]

What is the expected total amount of time in minutes the operator will spend on the calls each day

This is M, so:

[tex]M = n\mu = 75*2.8 = 210[/tex]

The expected total amount of time the operator will spend on the calls each day is of 210 minutes.

A grapefruit is 8% heavier than an orange, and an apple is 10% lighter than the
orange.
By what percentage is the grapefruit heavier than the apple?
pls answer

Answers

Grapefruit=108

Orange=100

Apple=90

a) (108-90)/90*100 = 18/90*100=20%

b) (108-90)/108= 18/108*100=16 2/3%

Answer:

The grapefruit is 20% heavier than the orange:)

Step-by-step explanation:

Let the weight of orange be x.

This means that the weight of grapefruit is:

       1.08x

( Since grapefruit is: 8% heavier than orange )

Also, the weight of apple is 10% lighter than apple.

This means that the weight of apple is: 0.90 x

Each time Caroline goes shopping she decides whether or not to buy fruit.
The probability that she does buy fruit is 0.6.
Independently, she then decides whether or not to buy a CD, with a probability of 0.2 that she does buy a CD.
Work out the probability that she buys fruit or buys a CD or both.

Answers

Answer:

this probability is 0.68

Step-by-step explanation:

the probability she buys fruit but not a CD is

0.6 × (1 - 0.2) = 0.48

the probability she buys a CD by not fruit is

0.2 × (1 - 0.6) = 0.08

the probability that she buys both is

0.6 × 0.2 = 0.12

the probability that she buys fruit or a CD or both is adding all 3 probabilities :

0.48 + 0.08 + 0.12 = 0.68

An College student complained that the cost of textbooks was too high. She randomly surveyed 36 other students and found that the mean amount of money spent for textbooks was $121.60. If the standard deviation of the population was $6.36, find the best point estimate. Show your work.

Answers

Answer:

The best point estimate for the mean amount of money spent for textbooks for all students at the College is of $121.60.

Step-by-step explanation:

Best point estimate:

The best point estimate of a population mean is the sample mean.

In this question:

The sample mean amount of money spent for textbooks was $121.60, which means that the best point estimate for the mean amount of money spent for textbooks for all students at the College is of $121.60.

Someone please help, thank you

Answers

Step-by-step explanation:

everything can be found in the picture

Answers:

(a) [tex]n = 2(r+m)[/tex]

(b) [tex]n = \frac{h^2}{9}[/tex]

===========================================

Work Shown:

Part (a)

[tex]\frac{n}{2} - m = r\\\\\frac{n}{2} = r+m\\\\n = 2(r+m)[/tex]

In the second step, I added m to both sides. Afterward, I multiplied both sides by 2 to fully isolate n.

------------------------

Part (b)

[tex]3\sqrt{n} = h\\\\\sqrt{n} = \frac{h}{3}\\\\n = \left(\frac{h}{3}\right)^2\\\\n = \frac{h^2}{3^2}\\\\n = \frac{h^2}{9}\\\\[/tex]

First I divided both sides by 3. After that, I squared both sides. The (h/3) squares to (h^2)/9.

Shen started to run on a treadmill after setting its timer for 93 minutes. The display says that he has finished 69% of his run. How many minutes have gone by?
Round your answer to the nearest tenth.

Answers

Answer:

64.2 minutes

Step-by-step explanation:

We are given that

Shen set timer to run=93 minutes

He has finished his run=69%

We have to find total number of minutes have gone by.

69% of 93

=[tex]\frac{69}{100}\times 93[/tex]

By using

a%[tex]=\frac{a}{100}[/tex]

69% of 93=[tex]\frac{6417}{100}[/tex]

69% of 93=64.17 min

69% of 93[tex]\approx 64.2min[/tex]

Hence, 64.2 minutes have gone by.

What is the sample space for the suits of a standard 52-card deck of cards?

Answers

Mark Brainliest please

All the possible outcomes of an experiment.

Example: choosing a card from a deck
There are 52 cards in a deck (not including Jokers)

So the Sample Space is all 52 possible cards: {Ace of Hearts, 2 of Hearts, etc... }

The sample space for the suits of a standard 52-card deck of cards is {Hearts, Diamonds, Clubs, Spades}.

What is Probability?

It is a branch of mathematics that deals with the occurrence of a random event.

The sample space for the suits of a standard 52-card deck of cards consists of four elements, one for each suit:

Hearts

Diamonds

Clubs

Spades

Each card in the deck belongs to one of these four suits. Therefore, the sample space for the suits of a standard 52-card deck of cards is {Hearts, Diamonds, Clubs, Spades}.

Hence, the sample space for the suits of a standard 52-card deck of cards is {Hearts, Diamonds, Clubs, Spades}.

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[3⋅5]7=


help pls anyone pls help me

Answers

The answer to ur question is 105

Is each statement true for parallelogram DEFG? Drag each statement into the correct box.
DF=EG
EF=DG
∠DEG ≅ ∠FGE

Answers

Yes all of them are true

The statements DF=EG, EF=DG and ∠DEG ≅ ∠FGE are true for parallelogram DEFG.

What is Quadrilateral?

a quadrilateral is a four-sided polygon, having four edges and four corners.

DEFG is a parallelogram.

A parallelogram is a simple quadrilateral with two pairs of parallel sides.

The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

DF=FG is a true statement.

The diagonal passing through a parallelogram are equal in length.

EF=DG is a true statement

The opposite sides of a parallelogram are equal.

∠DEG ≅ ∠FGE are congruent angles.

Because the opposite angles of a triangle are equal in meausure.

Hence, the statements DF=EG, EF=DG and ∠DEG ≅ ∠FGE are true for parallelogram DEFG.

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At a school camp there is enough foot for 150 students for 5 days.
Q: How long would the food last if there were only 100 students?

Answers

Answer:

Step-by-step explanation:

you need to find how much food is used for 1 person then times that answer by 100 to find how much food is needed

A binary operation is defined on the set of real numbers ℝ by

x ∆ y = x²− 2xy + y
²

; x, y ∈ ℝ.

i. Find m such that 2 ∆ − 5 = √m

ii. Simplify ((n+1) ∆ y)/n


; n ≠ 0​

Answers

Answer:

I. m = 2401

II. ((n+1) ∆ y)/n = 1/n[(n – y + 2)(n – y) + 1]

Step-by-step explanation:

I. Determination of m

x ∆ y = x² − 2xy + y²

2 ∆ − 5 = √m

2² − 2(2 × –5) + (–5)² = √m

4 – 2(–10) + 25 = √m

4 + 20 + 25 = √m

49 = √m

Take the square of both side

49² = m

2401 = m

m = 2401

II. Simplify ((n+1) ∆ y)/n

We'll begin by obtaining (n+1) ∆ y. This can be obtained as follow:

x ∆ y = x² − 2xy + y²

(n+1) ∆ y = (n+1)² – 2(n+1)y + y²

(n+1) ∆ y = n² + 2n + 1 – 2ny – 2y + y²

(n+1) ∆ y = n² + 2n – 2ny – 2y + y² + 1

(n+1) ∆ y = n² – 2ny + y² + 2n – 2y + 1

(n+1) ∆ y = n² – ny – ny + y² + 2n – 2y + 1

(n+1) ∆ y = n(n – y) – y(n – y) + 2(n – y) + 1

(n+1) ∆ y = (n – y + 2)(n – y) + 1

((n+1) ∆ y)/n = [(n – y + 2)(n – y) + 1] / n

((n+1) ∆ y)/n = 1/n[(n – y + 2)(n – y) + 1]

A circle P is circumscribed about a regular hexagon ABCDEF

Arcs AB, BC, CD, DE, EF, FA are all equal
Select one:
a. False
b. True

Answers

Answer: True

Explanation:

Let point G be the center of both the hexagon and the circle.

The measure of arc AB is the same as central angle AGB, both of which are 360/6 = 60 degrees. This applies to the other arc measures as well. The full 360 degree circle is split up into 6 equal pieces, each piece being 60 degrees.

+
= 1
Which ellipse has a major axis that is vertical?
A (x + 1)2 (y + 12)2
20
6
8 3x2 + 7y2 - 21 = 0
© An ellipse with foci (0, 15) and (0, -15) and co-vertices (4,0).and (-4, 0)
An ellipse with vertices (0, 4) and (30, 4) and co-vertices (15, 3) and (15,5)

Answers

Answer:

Step-by-step explanation:Bó tay

is the sum of two rational numbers sometimes zero ture or false?​

Answers

Answer:

True.

Step-by-step explana

-4/5 + 4/5 is 0

A money box contains only 10-cent
and 20-cent coins. There are 33
coins with a total value of $4.60.
How many coins of each?

Answers

Answer:

Below in bold.

Step-by-step explanation:

x + y = 33      where x = 10 cent coin and y = 20 cent coin

10x + 20y = 460

Multiply first equation by 10:

10x + 10y = 330

Subtract this from the second equation:

10y = 130

y = 13

So there are 13 20c coins

and 33 - 13 = 20 10c coins.

20 ten cents and 13 twenty cents
This is a real logic problem you just need to trial and error

Please help me ASAP ASAP ASAP

Answers

Answer:

d = 4√5

Step-by-step explanation:

d² = 8² + 4²

d² = 64 + 16

d² = 80

d =√80

d = √(16 * 5)

d = 4√5

Answer:

Step-by-step explanation:

hard to see graph ....

This is a 30-60-90 triangle. What is the measure of x?

Answers

X would be 7 radical 3

Discount Comics is running a special: 20 comics for $5.00. Seth purchases 30 comics for $7.50. What is the sale price per comic?
$ per comic?

Answers

Answer:

$0.25

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Write this ratio as a fraction in simplest form without any units. 6 weeks to 49 days You can use the table below to help convert the units.​

Answers

Step-by-step explanation:

6 weeks : 49 days

42 days : 49 days

42/49(HCF is 7, so divide both values by 7)

that will equal to 6/7

At the beginning of a population study, a city had 320,000 people. Each year since, the population has grown by 2.1%. Lett be the number of years since start of the study. Let y be the city's population. Write an exponential function showing the relationship between y and t. ​

Answers

Answer:

y = 320,000(2.1)^t

Step-by-step explanation:

uhm, im not very good at explaining, but everytime the year increases, the population will exponentially increase, that's why 't' is an exponent

Answer:

[tex]y=320000(1.021)^t[/tex]

Step-by-step explanation:

To increase something by x% mulitply it by (1+x)

in other words, to increase sometihng by 2.1% mulitply it by

(1+.021) or 1.021

because we are mulitplying 320000 by 1.021 each year we can write the equation as

y=320000(1.021)^t

For brainlest:)))) answer

Answers

Answer:

0

Step-by-step explanation:

There are not rotational symmetry.

Which region represents the solution to the given system of inequalities?

Answers

Answer:

The intersection region shown in the graph attached is the solution of the system of inequalities

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