Suppose x has a distribution with a mean of 90 and a standard deviation of 3. 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 normal a geometric an unknown a Poisson a binomial an approximately normal distribution with
mean μx =
and
standard deviation σx = .
(b) Find the z value corresponding to
x = 91.
z =
(c) Find
P(x < 91).
(Round your answer to four decimal places.)
P(x < 91) =
(d) Would it be unusual for a random sample of size 36 from the
x distribution to have a sample mean less than 91?
Explain.
No, it would not be unusual because less than 5% of all such samples have means less than 91.No, it would not be unusual because more than 5% of all such samples have means less than 91. Yes, it would be unusual because less than 5% of all such samples have means less than 91.Yes, it would be unusual because more than 5% of all such samples have means less than 91.
Solution :
Given that ,
mean = = 90
standard deviation = = 3
n = 36
a) has an approximately normal distribution with,
= = 90
= / n = 3 / 36 = 0.5
b) = 91
z = - ) /
z = 91 - 90 / 0.5
z = 2.00
c) 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 91.
Suppose x has a distribution with a mean of 90 and a standard deviation of 3....
Suppose x has a distribution with a mean of 50 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 distribution with mean μx = and standard deviation σx = . (b) Find the z value corresponding to x = 41. z = (c) Find P(x < 41). (Round your answer to four decimal places.) P(x < 41)...
Suppose x has a distribution with a mean of 90 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 has ---Select- distribution with meanz - and standard deviation o, - (b) Find the z value corresponding to x = 83. ZE (c) Find P(x < 83), (Round your answer to four decimal places.) P(x < 83) = (d) Would...
Suppose x has a distribution with a mean of 40 and a standard deviation of 20. Random samples of size n = 64 are drawn. (a) Describe the x bar distribution. x bar has a normal distribution. x bar has a geometric distribution. x bar has an approximately normal distribution. x bar has a Poisson distribution. x bar has an unknown distribution. x bar has a binomial 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 20. Random samples of size n = 64 are drawn. (a) Describe the distribution. x has a geometric distribution. has a normal distribution. x has an unknown distribution. x has a Poisson distribution. X has an approximately normal distribution. x has a binomial distribution. Compute the mean and standard deviation of the distribution. (For each answer, enter a number.) Hy = Oz = (b) Find...
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 distribution ___________ with mean μx = _______ and standard deviation σx = __________. (b) Find the z value corresponding to x = 79. z = (c) Find P(x < 79). (Round your answer to four decimal places.) P(x...
Suppose x has a distribution with μ = 82 and σ = 9. (a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means? Yes, the x distribution is normal with mean μx = 82 and σx = 0.6.No, the sample size is too small. Yes, the x distribution is normal with mean μx = 82 and σx = 2.25.Yes, the x distribution is normal with mean μx = 82...
6. Basic Computation: Central Limit Theorem Suppose x has a distribution with a mean of 20 and a standard deviation of 3. Random samples of size n 36 are drawn. (a) Describe the x distribution and compute the mean and standard deviation of the distribution. (b) Find the z value corresponding to x = 19. (c) Find P(x < 19). (d) Interpretation Would it be unusual for a random sample of size 36 from the x distribution to have a...
ORMAL CURVES AND SAMPLING DİSTRIBUTIONS Basic Computation: Central Limit Theorem Suppose x has a distributi on with a mean of 20 and a standard deviation of 3. Random samples of size n are drawn. (a) Describe the a distribution and compute the mean and standard deviation of the distribution. (b) Find the z value corresponding to x = 19. (c) Find Pr < 19) (d) Interpretation Would it be unusual for a random sample of size 36 from the x...
For samples of the specified size from the population described, find the mean and standard deviation of the sample mean x-bar. The mean and the standard deviation of the sampled population are, respectively, 182.1 and 29.4. n = 36 μx-bar = 29.4 and σx-bar = 4.9 μx-bar = 356.9 and σx-bar = 1.0 μx-bar = 182.1 and σx-bar = 4.9 μx-bar = 4.9 and σx-bar = 182.1
Suppose x has a distribution with μ = 20 and σ = 19. (a) If a random sample of size n = 42 is drawn, find μx, σx and P(20 ≤ x ≤ 22). (Round σx to two decimal places and the probability to four decimal places.) μx = σx = P(20 ≤ x ≤ 22) = (b) If a random sample of size n = 68 is drawn, find μx, σx and P(20 ≤ x ≤ 22). (Round σx...