Recall that the standard deviation is calculated using the formula ? = (x − ?)2P(x) , where x is the value of a random variable, ? is the expected value of x, P(x) is the probability of that variable, and the sum is taken for all values of the random variable.Consider the given distribution.x012P(x)0.500.300.20To simplify the calculation of ?, first determine (x − ?)2 for each value of x. Recall that we previously found ? = 0.7.x012(x − ?)2(0 − 0.7)2 = (1 − 0.7)2 = (2 − 0.7)2 = B. Consider the probability distribution shown below.x012P(x)0.450.400.15Compute the expected value of the distribution.Compute the standard deviation of the distribution. (Round your answer to four decimal places.)C.What is the age distribution of promotion-sensitive shoppers? A supermarket super shopper is defined as a shopper for whom at least 70% of the items purchased were on sale or purchased with a coupon.Age range, years18-2829-3940-5051-6162 and overMidpoint x2334455667Percent of super shoppers10%41%21%13%15%Compute the expected age ? of a super-shopper. (Round your answer to two decimal places.)? = yr(d)Compute the standard deviation ? for ages of super shoppers. (Round your answer to two decimal places.)? = yr D. What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Suppose we have the following information. Note: In 1851 there were 25,466 nurses in Great Britain.Age range (yr)20-2930-3940-4950-5960-6970-7980+Midpoint x24.534.544.554.564.574.584.5Percent of nurses5.3%9.9%19.1%29.8%25.4%8.5%2.0%Find the probability that a British nurse selected at random in 1851 would be 60 years of age or older. (Round your answer to three decimal places.)Compute the expected age ? of a British nurse contemporary to Florence Nightingale. (Round your answer to two decimal places.) yrCompute the standard deviation ? for ages of nurses shown in the distribution. (Round your answer to two decimal places.) yr

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Recall that the standard deviation is calculated using the formula

? =

	(x − ?)²P(x)

where x is the value of a random variable, ? is the expected value of x,

P(x)

is the probability of that variable, and the sum is taken for all values of the random variable.
Consider the given distribution.

x	0	1	2
P(x)	0.50	0.30	0.20

To simplify the calculation of ?, first determine (x − ?)²for each value of x. Recall that we previously found

? = 0.7.

x	0	1	2
(x − ?)²	(0 − 0.7)² =	(1 − 0.7)² =	(2 − 0.7)² =

B. Consider the probability distribution shown below.

x	0	1	2
P(x)	0.45	0.40	0.15

Compute the expected value of the distribution.

Compute the standard deviation of the distribution. (Round your answer to four decimal places.)

What is the age distribution of promotion-sensitive shoppers? A supermarket super shopper is defined as a shopper for whom at least 70% of the items purchased were on sale or purchased with a coupon.

Age range, years	18-28	29-39	40-50	51-61	62 and over
Midpoint x	23	34	45	56	67
Percent of super shoppers	10%	41%	21%	13%	15%

Compute the expected age ? of a super-shopper. (Round your answer to two decimal places.)

? = yr

(d)

Compute the standard deviation ? for ages of super shoppers. (Round your answer to two decimal places.)

? = yr

D. What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Suppose we have the following information. Note: In 1851 there were 25,466 nurses in Great Britain.

Age range (yr)	20-29	30-39	40-49	50-59	60-69	70-79	80+
Midpoint x	24.5	34.5	44.5	54.5	64.5	74.5	84.5
Percent of nurses	5.3%	9.9%	19.1%	29.8%	25.4%	8.5%	2.0%

Find the probability that a British nurse selected at random in 1851 would be 60 years of age or older. (Round your answer to three decimal places.)

Compute the expected age ? of a British nurse contemporary to Florence Nightingale. (Round your answer to two decimal places.)
yr

Compute the standard deviation ? for ages of nurses shown in the distribution. (Round your answer to two decimal places.)
yr

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