Question

Suppose x has a distribution with a mean of 50 and a standard deviation of 15. 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 an approximately normal distribution. x bar has a Poisson distribution. x bar has a geometric distribution. x bar has a normal distribution. Compute the mean and standard deviation of the distribution. (For each answer, enter a number.) mu sub x bar = mu sub x bar = sigma sub x bar = sigma sub x bar =

(b) Find the z value corresponding to x bar = 55. (Enter an exact number.) z =

(c) Find P(x bar < 55). (Enter a number. Round your answer to four decimal places.) P(x bar < 55) = P(x bar < 55)

(d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 55?

Explain.

Yes, it would be unusual because more than 5% of all such samples have means less than 55.

No, it would not be unusual because more than 5% of all such samples have means less than 55.

Yes, it would be unusual because less than 5% of all such samples have means less than 55.

No, it would not be unusual because less than 5% of all such samples have means less than 55.

Answer 1

Solution :

Given that,

mean = = 50

standard deviation = = 15

n = 36

a)    has an approximately normal distribution.

=    = 50

= / n = 15/ 36 = 2.5

b) = 55

z = - /

z = 55 - 50 / 2.5

z = 2.00

c) P( < 55) = P(( - ) / < (55 - 50) / 2.5)

= P(z < 2.00)

Using z table

= 0.9772

d) No, it would not be unusual because more than 5% of all such samples have means less than 55.