Question

In: Math

Suppose x has a distribution with μ = 65 and σ = 9. (a) If random...

Suppose x has a distribution with μ = 65 and σ = 9.

(a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means?

No, the sample size is too small.Yes, the x distribution is normal with mean μ_x = 65 and σ_x = 9. Yes, the x distribution is normal with mean μ_x = 65 and σ_x = 0.6.Yes, the x distribution is normal with mean μ_x = 65 and σ_x = 2.25.

(b) If the original x distribution is normal, can we say anything about the x distribution of random samples of size 16?

No, the sample size is too small.Yes, the x distribution is normal with mean μ_x = 65 and σ_x = 2.25. Yes, the x distribution is normal with mean μ_x = 65 and σ_x = 9.Yes, the x distribution is normal with mean μ_x = 65 and σ_x = 0.6.

Find P(61 ≤ x ≤ 66). (Round your answer to four decimal places.)

Expert Solution

Solution :

Given that,

mean = = 65

standard deviation = = 9

n=16

= 65

= / n = 9 / 16=2.25

es, the x distribution is normal with mean μ_x = 65 and σ_x = 2.25.

= P(61< <66 ) = P[(61 - 65) /2.25 < ( - ) / < (66 - 65) /2.25 )]

= P( -1.78< Z < 0.44)

= P(Z <0.44 ) - P(Z <-1.78 )

Using z table,

= 0.6700 -0.0375

= 0.6325

milcah answered 2 years ago

Suppose x has a distribution with μ = 17 and σ = 9.(a) If a random...

Suppose x has a distribution with μ = 17 and σ = 9.(a) If a random sample of size n = 45 is drawn, find μx, σ x and P(17 ≤ x ≤ 19). (Round σx to two decimal places and the probability to four decimal places.)μx = σ x = P(17 ≤ x ≤ 19) = (b) If a random sample of size n = 72 is drawn, find μx, σ x and P(17 ≤ x ≤ 19). (Round...

Suppose x has a distribution with μ = 12 and σ = 9. A.) If a...

Suppose x has a distribution with μ = 12 and σ = 9. A.) If a random sample of size n = 35 is drawn, find μx, σx and P(12 ≤ x ≤ 14). (Round σx to two decimal places and the probability to three decimal places.) P(12 ≤ x ≤ 14)= B.) If a random sample of size n = 62 is drawn, find μx, σx and P(12 ≤ x ≤ 14). (Round σx to two decimal places and...

33) Suppose x has a distribution with μ = 84 and σ = 9. (a) If...

33) Suppose x has a distribution with μ = 84 and σ = 9. (a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means? No, the sample size is too small. Yes, the x distribution is normal with mean μ x = 84 and σ x = 2.25. Yes, the x distribution is normal with mean μ x = 84 and σ x = 0.6. Yes, the x...

Suppose x has a distribution with μ = 35 and σ = 14. (a) If random...

Suppose x has a distribution with μ = 35 and σ = 14. (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 = 35 and σx = 0.9.No, the sample size is too small. Yes, the x distribution is normal with mean μx = 35 and σx = 3.5.Yes, the x distribution is normal with mean μx = 35...

Suppose x has a distribution with μ = 84 and σ = 15. (a) If random...

Suppose x has a distribution with μ = 84 and σ = 15. (a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means? No, the sample size is too small.Yes, the x distribution is normal with mean μx = 84 and σx = 0.9. Yes, the x distribution is normal with mean μx = 84 and σx = 3.75.Yes, the x distribution is normal with mean μx = 84...

Suppose x has a distribution with μ = 35 and σ = 20. (a) If random...

Suppose x has a distribution with μ = 35 and σ = 20. (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 = 35 and σx = 1.3.Yes, the x distribution is normal with mean μx = 35 and σx = 5. No, the sample size is too small.Yes, the x distribution is normal with mean μx = 35...

Suppose x has a distribution with μ = 40 and σ = 15. (a) If random...

Suppose x has a distribution with μ = 40 and σ = 15. (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 = 40 and σx = 15.Yes, the x distribution is normal with mean μx = 40 and σx = 0.9. Yes, the x distribution is normal with mean μx = 40 and σx = 3.75.No, the sample...

Suppose x has a distribution with μ = 59 and σ = 15. (a) If random...

Suppose x has a distribution with μ = 59 and σ = 15. (a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means? Multiple choice answers. Yes, the x distribution is normal with mean μx = 59 and σx = 0.9. Yes, the x distribution is normal with mean μx = 59 and σx = 3.75. No, the sample size is too small. Yes, the x distribution is...

Suppose x has a distribution with μ = 31 and σ = 15. (a) If random...

Suppose x has a distribution with μ = 31 and σ = 15. (a) If random samples of size n = 16 are selected, can we say anything about the x distribution of sample means? (b) If the original x distribution is normal, can we say anything about the x distribution of random samples of size 16? (c) Find P(27 ≤ x ≤ 32). (Round your answer to four decimal places.)

Suppose x has a distribution with μ = 20 and σ = 5. (a) If random...

Suppose x has a distribution with μ = 20 and σ = 5. (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 μ x = 20 and σ x = 1.25. No, the sample size is too small. Yes, the x distribution is normal with mean μ x = 20 and σ x = 5. Yes, the x distribution...