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labwork [276]
3 years ago
7

The weekly amount spent by a small company for in-state travel has approximately a normal distribution with mean $1450 and stand

ard deviation $220. What is the probability that the actual expenses will exceed $1560 in 20 or more weeks during the next year?
Mathematics
1 answer:
Llana [10]3 years ago
7 0

Answer:

0.0903

Step-by-step explanation:

Given that :

The mean = 1450

The standard deviation = 220

sample mean = 1560

P(X > 1560) = P( Z > \dfrac{x - \mu}{\sigma})

P(X > 1560) = P(Z > \dfrac{1560 - 1450}{220})

P(X > 1560) = P(Z > \dfrac{110}{220})

P(X> 1560) = P(Z > 0.5)

P(X> 1560) = 1 - P(Z < 0.5)

From the z tables;

P(X> 1560) = 1 - 0.6915

P(X> 1560) = 0.3085

Let consider the given number of weeks = 52

Mean \mu_x = np = 52 × 0.3085 = 16.042

The standard deviation =  \sqrt {n \time p (1-p)}

The standard deviation = \sqrt {52 \times 0.3085 (1-0.3085)}

The standard deviation = 3.3306

Let Y be a random variable that proceeds in a binomial distribution, which denotes the number of weeks in a year that exceeds $1560.

Then;

Pr ( Y > 20) = P( z > 20)

Pr ( Y > 20) = P(Z > \dfrac{20.5 - 16.042}{3.3306})

Pr ( Y > 20) = P(Z >1 .338)

From z tables

P(Y > 20) \simeq 0.0903

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Step-by-step explanation:

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3 years ago
On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded annually, and Lana invested 2,000 at 5 percent a
Zepler [3.9K]

Answer:

A. $5

Step-by-step explanation:

Tim: 1000 x (1 + 0.10)² = 1210

Interest: 1210 - 1000 = 210

Lana: 2000 x (1 + 0.05)² = 2205

interest': 2205 - 2000 = 205

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8 0
3 years ago
3 A farmer has 580 square bales of hay in his shed with total mass 9850 kg.
rusak2 [61]

Answer:

a) 580 - 16n

b) 9850 - 271.72n

Step-by-step explanation:

a) starting number of bales = 580

each day, the farmer feeds out 2 bales of hay to each yard. he has 8 yards, so he feeds out 2 bales 8 times for a total of 2 * 8 = 16 bales. Therefore, he loses 16 bales each day

After the first day, he has 580-16 = 564 bales. After the second, he has 564-16 = 548 bales, and so on. He loses 16 bales n times for n days, and as a result, his final amount of bales is

original amount - amount lost = 580 - 16n

b)

First, we can calculate how much a bale weighs.

average = sum/count = 9850 kg / 580 ≈ 17 kg

Therefore, as he loses 16 bales of hay, he loses 17 kg 16 times, or approximately 271.72 kg of hay every day. For n days, he loses 271.72n kg. This brings his final amount to be

starting - amount lost = 9850 - 271.72n

4 0
3 years ago
I need help on #10. I figured the other ones out
GalinKa [24]
First, find the ratio between the two polygons. Lets take segment MG and TV since they are congruent. MG is 4, TV is 3. The ratio of MG to TV is 4:3. We can write it as 4/3. Since other arts are congruent as well, then NK is congruent to PR, and has a ratio of 4:3. This means that (3x-2)/(x+4) is equal to 4/3. Now solve for x
(3x-2)/(x+4)=4/3 
3(3x-2)=4(x+4)         ---cross multiply
9x-6=4x+16
9x-4x-6=4x-4x+16    ---subtract 4x from both sides
5x-6=16
5x-6+6=16+6            ---add 6 on both sides
5x=22
5x/5=22/5                 ---divide 5 on both sides
x=22/5

6 0
3 years ago
What is 1/3 into decimal form
elena-14-01-66 [18.8K]

Answer: 0.333

Step-by-step explanation:

4 0
3 years ago
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