Question

Suppose x has a distribution with a mean of 70 and a standard deviation of 3. Random samples of size n = 36 are drawn.

(a) Describe the x bar distribution.

-x bar has an unknown distribution.

-x bar has a binomial distribution.

-x bar has a Poisson distribution.

-x bar has a geometric distribution.

-x bar has a normal distribution.

-x bar has an approximately normal distribution.

Compute the mean and standard deviation of the distribution. (For each answer, enter a number.)

u x bar =_________

o x bar =_________

b) Find the z value corresponding to x bar = 71. (Enter an exact number.)

z =_____________

(c) Find P(x bar < 71). (Enter a number. Round your answer to four decimal places.) P(x bar < 71) = ______________

(d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 71? Explain.

-Yes, it would be unusual because more than 5% of all such samples have means less than 71.

-No, it would not be unusual because more than 5% of all such samples have means less than 71.

-No, it would not be unusual because less than 5% of all such samples have means less than 71.

-Yes, it would be unusual because less than 5% of all such samples have means less than 71.

Answer 1

Solution :

Given that ,

mean = = 70

standard deviation = = 3

n = 36

(a)x bar has a normal distribution.

= 70

= / n = 3 / 36 =0.5

(b) z = -   / = 71 - 70 / 0.5 = 2

(c)P( <71 ) = P(( - ) / < (71 - 70) / 0.5)

= P(z < 2)

Using z table

= 0.9772