Suppose that a random sample of size 64 is to be selected from a population with mean 40 and standard deviation 5. (a) What are the mean and standard deviation of the sampling distribution? μx = σx = (b) What is the approximate probability that x will be within 0.3 of the population mean μ? (Round your answer to four decimal places.) P = (c) What is the approximate probability that x will differ from μ by more than 0.6? (Round your answer to four decimal places.)

a) 0.625

b) 0.2510

c) 0.2005

Step-by-step explanation:

Data provided in the question:

Sample size, n = 64

Mean = 40

Standard deviation = 5

a) Mean of the sampling distribution = Sample mean = 40

Standard deviation of the sampling distribution =

=

= 0.625

b)

(from standard normal table)

c)

(from standard normal table)

angle addition postulate

2x=56

step-by-step explanation:

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true