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2 years ago

10

Your promotional budget for the year is $300 for personal selling, $300 for sales promotion, \$1,500 for advertising, and $500 f

or image promotion. What is your total promotional budget for this year?
a) $2,000

b) $2,600

c) $3,600

d) $4,600

1 answer:

aleksandr82 [10.1K]2 years ago

8 0

Answer:

to get the total promotion budget for the year we will add $300 for personal selling plus $300 for sales promotion plus $1500 for advertising plus $500 for image promotion to the a total of 2600 dollars

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Rocky Mountain National Park is a popular park for outdoor recreation activities in Colorado. According to U.S. National Park Se

Ugo [173]

Answer:

a) 0.6628 = 66.28% probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance

b) 0.5141 = 51.41% probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance

c) 0.5596 = 55.96% probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance.

d) 0.9978 = 99.78% probability that more than 55 visitors have no recorded point of entry

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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 pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 175$

(a) What is the probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance?

46.7% of visitors to Rocky Mountain National Park in 2018 entered through the Beaver Meadows. This means that $p = 0.467$ . So

$\mu = E(X) = np = 175*0.467 = 81.725$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.467*0.533} = 6.6$

This probability, using continuity correction, is $P(X \geq 85 - 0.5) = P(X \geq 84.5)$ , which is 1 subtracted by the pvalue of Z when X = 84.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{84.5 - 81.725}{6.6}$

$Z = 0.42$

$Z = 0.42$ has a pvalue of 0.6628.

66.28% probability that at least 85 visitors had a recorded entry through the Beaver Meadows park entrance.

(b) What is the probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance?

Using continuity correction, this is $P(80 - 0.5 \leq X < 90 - 0.5) = P(79.5 \leq X \leq 89.5)$ , which is the pvalue of Z when X = 89.5 subtracted by the pvalue of Z when X = 79.5. So

X = 89.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{89.5 - 81.725}{6.6}$

$Z = 1.18$

$Z = 1.18$ has a pvalue of 0.8810.

X = 79.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{79.5 - 81.725}{6.6}$

$Z = -0.34$

$Z = -0.34$ has a pvalue of 0.3669.

0.8810 - 0.3669 = 0.5141

51.41% probability that at least 80 but less than 90 visitors had a recorded entry through the Beaver Meadows park entrance

(c) What is the probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance?

6.3% of visitors entered through the Grand Lake park entrance, which means that $p = 0.063$

$\mu = E(X) = np = 175*0.063 = 11.025$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.063*0.937} = 3.2141$

This probability, using continuity correction, is $P(X < 12 - 0.5) = P(X < 11.5)$ , which is the pvalue of Z when X = 11.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{11.5 - 11.025}{3.2141}$

$Z = 0.15$

$Z = 0.15$ has a pvalue of 0.5596.

55.96% probability that fewer than 12 visitors had a recorded entry through the Grand Lake park entrance.

(d) What is the probability that more than 55 visitors have no recorded point of entry?

22.7% of visitors had no recorded point of entry to the park. This means that $p = 0.227$

$\mu = E(X) = np = 175*0.227 = 39.725$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{175*0.227*0.773} = 5.54$

Using continuity correction, this probability is $P(X \leq 55 + 0.5) = P(X \leq 55.5)$ , which is the pvalue of Z when X = 55.5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{55.5 - 39.725}{5.54}$

$Z = 2.85$

$Z = 2.85$ has a pvalue of 0.9978

0.9978 = 99.78% probability that more than 55 visitors have no recorded point of entry

8 0

2 years ago

Dividends Per Share Seventy-Two Inc., a developer of radiology equipment, has stock outstanding as follows: 60,000 shares of cum

anygoal [31]

Answer and Step-by-step explanation:

The computation of dividends per share on each class of stock for each of the four years is shown below:-

Particulars 1st year 2nd-year 3rd-year 4th year

Preferred dividend

paid a $34,000 $38,000 $36,000 $36,000

Number of preferred

stock b 60,000 60,000 60,000 60,000

Dividend per share

(a ÷ b) $0.57 $0.63 $0.60 $0.60

Dividend paid to common

stockholders c $0 $38,000 $44,000 $64,000

Number of common stock

shares d 410,000 410,000 410,000 410,000

Dividend per share

on common stock $0 $0.093 $0.11 $0.16

(c ÷ d)

Working note:

Preferred dividend = Number of preferred stock shares × Par value per share × Percentage of dividend

= 60,000 × $20 × 3%

= $36,000

Preferred stock

For 1st year

= $34,000

For 2nd-year

Dividend in year 2+ Dividend balance in year 1

= $36,000 + ($36,000 - $34,000)

= $38,000

For 3rd-year

= $36,000

For 4th year

= $36,000

Common stock dividend

Particulars 1 year 2 year 3 year 4 year

Total dividend paid $34,000 $76,000 $80,000 $100,000

Less:

Preferred stock

dividend $34,000 $38,000 $36,000 $36,000

Dividend paid to common

stockholders $0 $38,000 $44,000 $64,000

8 0

2 years ago

Malcolm and Ravi raced each other.

Semenov [28]

Malcolm maximum speed is 200 km/h and Ravi maximum speed is 320 km/h

Step-by-step explanation:

Lets assume Malcolm maximum speed to be M km/h and Ravi maximum speed to be R km/h

Average of their maximum speed is; (M+R)/2 =260 km/h

This can be simplified to M+R= 260*2

M+R = 520.......................................(I)

When Malcolm's speed is doubled,

2M=R+80 km/h ----------------------(ii)

The two equations are;

M+R = 520 ------ M=520-R ----(i)

2M=R+80 ---------------------------(ii)

Replacing M with (i) above

2M=R+80

2(520-R) =R+80

1040 -2R =R+80

1040-80 = R+2R

960 = 3R

960/3 =R

320 =R

M+R =520

M=520-320 =200

Malcolm maximum speed is 200 km/h and Ravi maximum speed is 320 km/h

Learn More

Simultaneous equations:brainly.com/question/12919422

Keywords: Average, maximum, speeds, doubled,

#LearnwithBrainly

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2 years ago

17. A local university accepted 2,300 students out of 4,500 applicants for admission. What was the acceptance rate, expressed as

Alona [7]

The answer is 51%
Because you have to divide 2,300/4500=0.51 which gives you 51%

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A chemist mixes different concentrations of

maks197457 [2]

Answer:

10 oz

Step-by-step explanation:

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