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Xelga [282]
3 years ago
9

Suppose 100 stastisticians attended a conference of the American Statistical Society. At the dinner, among the menu options were

a Caesar salad, roast beef, and apple pie. 35 had the Caesar salad, 28 had the roast beef, and 45 had the apple pie for dessert. Also, 15 had at least two of those three offerings, and 2 had all three. How many attendees had none of the three

Mathematics
1 answer:
miv72 [106K]3 years ago
3 0

Answer: 26 attendees had none of the three.

Step-by-step explanation:

The Venn diagram illustrating the situation is shown in the attached photo.

C represents the set of statisticians that had Caesar salad.

R represents the set of statisticians that had roast beef.

A represents the set of statisticians that had apple pie for dessert.

x represents the number that had Caesar salad and apple pie for dessert only.

y represents the number that had Caesar salad and roast beef.

z represents the number that had roast beef and apple pie for dessert only.

If 15 had at least two of those three offerings,it means that

x + y + z = 15

Therefore,

35 - (x + y + 2) + 28 - (y + z + 2) + 45 - (x + z + 2) + 2 + none = 100

35 - x - y - 2 + 28 - y - z - 2 + 45 - x - z - 2 + 2 + none = 100

35 + 28 + 45 - x - x - y - y - z - z - 2 - 2 - 2 + 2 + none = 100

108 - 2x - 2y - 2z - 4 + none = 100

108 - 4 - 2(x + y + z) + none = 100

Since x + y + z = 15, then

104 - 2(15) + none = 100

74 + none = 100

none = 100 - 74 = 26

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Please answer this correctly
borishaifa [10]

Answer:

47

Step-by-step explanation:

The probability for tails to land is 1/2 when you flip 1 coin.

When you flip 94 times, 1/2 × 94

= 47

6 0
3 years ago
Based on historical data, your manager believes that 26% of the company's orders come from first-time customers. A random sample
scoundrel [369]

Answer:

\hat p \sim N( p, \sqrt{\frac{p (1-p)}{n}})

And we can use the z score formula given by:

z = \frac{\hat p -\mu_p}{\sigma_p}

And if we find the parameters we got:

\mu_p = 0.26

\sigma_p = \sqrt{\frac{0.26(1-0.26)}{158}} = 0.0349

And we can find the z score for the value of 0.4 and we got:

z = \frac{0.4-0.26}{0.0349}= 4.0119

And we can find this probability:

P(z>4.0119) = 1-P(z

And if we use the normal standard table or excel we got:

P(z>4.0119) = 1-P(z

Step-by-step explanation:

For this case we have the following info given:

p = 0.26 represent the proportion of the company's orders come from first-time customers

n=158 represent the sample size

And we want to find the following probability:

p(\hat p >0.4)

And we can use the normal approximation since we have the following two conditions:

1) np = 158*0.26 = 41.08>10

2) n(1-p) = 158*(1-0.26) = 116.92>10

And for this case the distribution for the sample proportion is given by:

\hat p \sim N( p, \sqrt{\frac{p (1-p)}{n}})

And we can use the z score formula given by:

z = \frac{\hat p -\mu_p}{\sigma_p}

And if we find the parameters we got:

\mu_p = 0.26

\sigma_p = \sqrt{\frac{0.26(1-0.26)}{158}} = 0.0349

And we can find the z score for the value of 0.4 and we got:

z = \frac{0.4-0.26}{0.0349}= 4.0119

And we can find this probability:

P(z>4.0119) = 1-P(z

And if we use the normal standard table or excel we got:

P(z>4.0119) = 1-P(z

8 0
2 years ago
you work from 7:00 am to 11:00 am and from 12:00pm to 4:00 pm. your hourly rate is $7.50. You do not work overtime. Find the hou
Viktor [21]

Answer:

Worked 40 hrs in week

Pay $300 for week

Step-by-step explanation:

Hours: 7-11a.m = 4

12-4p.m = 4 So, 4+4=8 hrs per day

So, 8 hrs per day × 5 days a week (8×5)=40

Worked 40 hrs in week

Pay: $7.50/hr So, $7.50×40 hrs (7.50×40)=300

So, $300 pay for week

7 0
3 years ago
Daniel borrowed $8,000 at 6% interest for 10 years. What was the total interest?   A. $48,000   B. $4,800   C. $480   D. $48
Mariulka [41]
I think it wold be b

please tell me if i wrong
4 0
3 years ago
Dr. Betz, a vet, is running a free rabies clinic. He estimates that it will take him 12 minutes for each animal he treats. Dr. B
Olin [163]

Answer:

equation: y = 12x

Dr. Betz worked for 8 hours.

Step-by-step explanation:

To write the equation we'll use the form y = mx, where y represents the amount of time the Doctor worked, m is the amount of minutes it takes to treat each animal, and x is how many animals have been treated. We know the value of m is 12, so let's put that into the equation:

y = 12x

Now we have our equation. We can use it to see how long Dr. Betz worked. He treated a total of 40 animals - 20 including the shaggy dog, and 20 after the shaggy dog. let's replace x with 40:

y = 12(40)

Now solve:

y = 480

Dr. Betz worked for 480 minutes. There are 60 minutes in an hour. Divide 480 by 60 to find out how many hours Dr. Betz worked for:

480/60 = 8

Dr. Betz worked for 8 hours.

7 0
3 years ago
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