Question

In: Statistics and Probability

X1, X2, ... , X34 is a random sample from a distribution with mean μ =...

X₁, X₂, ... , X₃₄ is a random sample from a distribution with mean μ = 7.26 and variance σ² = 13.10

1) Find P(X ≤6.13)

2) Find P(X >6.13)

3) Find P(6.85 < X≤ 7.85)

Solutions

Expert Solution

Solution :

Given that ,

= 7.26

2 = 13.10

= 2 = 13.10 = 3.62

= / n = / 34 = 0.62

a) P( 6.13 ) = P(( - ) / (6.13 - 7.26) / 0.62)

= P(z -1.82)

Using z table

= 0.0344

b) P( > 6.13) = 1 - P( < 6.13 )

= 1 - P[( - ) / < (6.13 - 7.26) / 0.62]

= 1 - P(z < -1.82 )

= 1 - 0.0344

= 0.9656

c) P(6.85 < 7.85)

= P[(6.85 - 7.26) / 0.62 < ( - ) / (7.85 - 7.26) / 0.62)]

= P(-0.66 < Z 0.95)

= P(Z 0.95) - P(Z < -0.66 )

Using z table,

= 0.8289 - 0.2546

= 0.5743

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Let X1,X2,...,Xn be a random sample from any distribution with mean μ and moment generating function...

Let X1,X2,...,Xn be a random sample from any distribution with mean μ and moment generating function M(t). Assume that M(t) is finite for some t > 0. Let c>μ be any constant. Let Yn = X1+X2+···+Xn. Show that P(Yn ≥ cn) ≤ exp[−n a(c)] where P(Yn ≥ cn) ≤ exp[−n a(c)] a(c) = sup[ct − ln M (t)]. t > 0

Suppose X1, X2, , ... , X10is a random sample from a distribution with mean u...

Suppose X1, X2, , ... , X10is a random sample from a distribution with mean u and variance 6. Also, is a random sample from a distribution with mean u and variance 30. These samples are independent as well. a. Is 0.2X + 0.8Y unbiased? Cannot be determined from this information or Yes or No b. What is the MSE of u? Round to 2 decimals. c. Based on the MSE criterion, is mu (u ), X (x bar), or Y (y...

Let x1, x2,x3,and x4 be a random sample from population with normal distribution with mean ?...

Let x1, x2,x3,and x4 be a random sample from population with normal distribution with mean ? and variance ?2 . Find the efficiency of T = 17 (X1+3X2+2X3 +X4) relative to x= x/4 , Which is relatively more efficient? Why?

Let X1,X2, . . . , Xn be a random sample from the uniform distribution with...

Let X1,X2, . . . , Xn be a random sample from the uniform distribution with pdf f(x; θ1, θ2) = 1/(2θ2), θ1 − θ2 < x < θ1 + θ2, where −∞ < θ1 < ∞ and θ2 > 0, and the pdf is equal to zero elsewhere. (a) Show that Y1 = min(Xi) and Yn = max(Xi), the joint sufficient statistics for θ1 and θ2, are complete. (b) Find the MVUEs of θ1 and θ2.

Suppose X1, X2, . . . , Xn is a random sample from N(μ, 16). Find...

Suppose X1, X2, . . . , Xn is a random sample from N(μ, 16). Find the maximum likelihood estimator of the 95th percentile.

Let X1, X2, . . . , Xn represent a random sample from a Rayleigh distribution...

Let X1, X2, . . . , Xn represent a random sample from a Rayleigh distribution with pdf f(x; θ) = (x/θ) * e^x^2/(2θ) for x > 0 (a) It can be shown that E(X2 P ) = 2θ. Use this fact to construct an unbiased estimator of θ based on n i=1 X2 i . (b) Estimate θ from the following n = 10 observations on vibratory stress of a turbine blade under specified conditions: 16.88 10.23 4.59 6.66...

Let X1, X2, ..., Xn be a random sample of size from a distribution with probability...

Let X1, X2, ..., Xn be a random sample of size from a distribution with probability density function f(x) = λxλ−1 , 0 < x < 1, λ > 0 a) Get the method of moments estimator of λ. Calculate the estimate when x1 = 0.1, x2 = 0.2, x3 = 0.3. b) Get the maximum likelihood estimator of λ. Calculate the estimate when x1 = 0.1, x2 = 0.2, x3 = 0.3.

. Let X1, X2, ..., Xn be a random sample of size 75 from a distribution...

. Let X1, X2, ..., Xn be a random sample of size 75 from a distribution whose probability distribution function is given by f(x; θ) = ( 1 for 0 < x < 1, 0 otherwise. Use the central limit theorem to approximate P(0.45 < X < 0.55)

For questions 1-5, X1, X2, ... , X23 is a random sample from a distribution with...

For questions 1-5, X1, X2, ... , X23 is a random sample from a distribution with mean μ = -1.02 and variance σ2 = 0.62. For questions 5-10, X1, X2, ... , X28 is a random sample from a distribution with mean μ = -8.77 and variance σ2 = 1.28. 1. Find μx, the mean of the sample average. 2. Find σ2x, the variance of the sample average. 3. Find P(X ≤ -1.14). 4. Find P(X > -1.14). 5. Find...

Suppose X1, . . . , Xn is a random sample from the Normal(μ, σ2) distribution,...

Suppose X1, . . . , Xn is a random sample from the Normal(μ, σ2) distribution, where μ is unknown but σ2 is known, and it is of interest to test H0: μ = μ0 versus H1: μ ̸= μ0 for some value μ0. The R code below plots the power curve of the test Reject H0 iff |√n(X ̄n − μ0)/σ| > zα/2 for user-selected values of μ0, n, σ, and α. For a sequence of values of μ,...

Subjects