Question

In: Statistics and Probability

Suppose x has a distribution with a mean of 90 and a standard deviation of 36....

Suppose x has a distribution with a mean of 90 and a standard deviation of 36. Random samples of size n = 64 are drawn.

(a) Describe the x-bar distribution and compute the mean and standard deviation of the distribution.

x-bar has _____ (an approximately normal, a binomial, an unknown, a normal, a Poisson, a geometric) distribution with

mean μx-bar = _____ and standard deviation σx-bar = _____ .


(b) Find the z value corresponding to

x-bar = 99.

z = _____


(c) Find

P(x-bar < 99). (Round your answer to four decimal places.)

P(x-bar < 99) = _____



(d) Would it be unusual for a random sample of size 64 from the x distribution to have a sample mean less than 99? Explain.

No, it would not be unusual because more than 5% of all such samples have means less than 99.

No, it would not be unusual because less than 5% of all such samples have means less than 99.

Yes, it would be unusual because less than 5% of all such samples have means less than 99.

Yes, it would be unusual because more than 5% of all such samples have means less than 99.

Solutions

Expert Solution

Solution :

Given that ,

mean = = 90

standard deviation = = 36

n = 64

a) is approximately normal

=   = 90

= / n = 36 / 64 = 4.5

b) = 99

Using z-score formula,

z = -   /

z = 99 - 90 / 4.5

z = 2.00

c) P( < 99) = P(( - ) / < (99 - 90) / 4.5)

= 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 99.


Related Solutions

Suppose x has a distribution with a mean of 90 and a standard deviation of 12....
Suppose x has a distribution with a mean of 90 and a standard deviation of 12. Random samples of size n = 64 are drawn. (a) Describe the x bar 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 unknown distribution. x bar has an approximately normal distribution. Compute the mean and standard deviation of the distribution. (For each answer,...
Suppose x has a normal distribution with mean μ = 36 and standard deviation σ =...
Suppose x has a normal distribution with mean μ = 36 and standard deviation σ = 5. Describe the distribution of x values for sample size n = 4. (Round σx to two decimal places.) μx = σx = Describe the distribution of x values for sample size n = 16. (Round σx to two decimal places.) μx = σx = Describe the distribution of x values for sample size n = 100. (Round σx to two decimal places.) μx...
Suppose x has a distribution with a mean of 70 and a standard deviation of 52....
Suppose x has a distribution with a mean of 70 and a standard deviation of 52. Random samples of size n = 64 are drawn. (a) Describe the x distribution and compute the mean and standard deviation of the distribution. x has distribution with mean μx = and standard deviation σx = . (b) Find the z value corresponding to x = 83. z = (c) Find P(x < 83). (Round your answer to four decimal places.) P(x < 83)...
Suppose x has a distribution with a mean of 70 and a standard deviation of 3....
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,...
Suppose x has a distribution with a mean of 40 and a standard deviation of 21....
Suppose x has a distribution with a mean of 40 and a standard deviation of 21. Random samples of size n = 36 are drawn. (a) Describe the x distribution and compute the mean and standard deviation of the distribution. x has distribution with mean μx = and standard deviation σx = . (b) Find the z value corresponding to x = 47. z = (c) Find P(x < 47). (Round your answer to four decimal places.) P(x < 47)...
Suppose x has a distribution with a mean of 40 and a standard deviation of 28....
Suppose x has a distribution with a mean of 40 and a standard deviation of 28. Random samples of size n = 64 are drawn. (a) Describe the x distribution and compute the mean and standard deviation of the distribution. x has  ---Select--- a binomial an approximately normal a normal a geometric an unknown a Poisson distribution with mean μx = ? and standard deviation σx =  .? (b) Find the z value corresponding to x = 33. z = c) Find...
Suppose x has a distribution with a mean of 60 and a standard deviation of 21....
Suppose x has a distribution with a mean of 60 and a standard deviation of 21. Random samples of size n = 36 are drawn. (a) Describe the x bar distribution. Compute the mean and standard deviation of the distribution. (For each answer, enter a number.) (b) Find the z value corresponding to x bar = 53. (c) Find P(x bar < 53). (Enter a number. Round your answer to four decimal places.) (d) Would it be unusual for a...
Suppose x has a distribution with a mean of 70 and a standard deviation of 27....
Suppose x has a distribution with a mean of 70 and a standard deviation of 27. Random samples of size n = 36 are drawn. (a) Describe the x distribution and compute the mean and standard deviation of the distribution. x has  ---Select--- a binomial a geometric a Poisson a normal an approximately normal an unknown distribution with mean μx = and standard deviation σx =  . (b) Find the z value corresponding to x = 61. z = (c) Find P(x...
Suppose x has a distribution with a mean of 50 and a standard deviation of 15....
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,...
Suppose x has a distribution with a mean of 70 and a standard deviation of 51....
Suppose x has a distribution with a mean of 70 and a standard deviation of 51. Random samples of size n = 36 are drawn. (a) Describe the  distribution. has a binomial distribution. has an approximately normal distribution.     has a geometric distribution. has a normal distribution. has an unknown distribution. has a Poisson distribution. (b) Compute the mean and standard deviation of the distribution. (For each answer, enter a number.) = = What price do farmers get for their watermelon crops?...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT