Question

Suppose that Upper X has a discrete uniform distribution f left-parenthesis x right-parenthesis equals StartLayout left-brace1st Row 1st Column 1 divided by 3, 2nd Column x equals 1,2,3 2nd Row 1st Column 0, 2nd Column otherwise EndLayout A random sample of n equals 35 is selected from this population. Find the probability that the sample mean is greater than 2.1 but less than 2.6. Express the final answer to four decimal places (e.g. 0.9876). The probability is

Answer #1

x | f(x) | yP(x) |
x^{2}P(x) |

1 | 1/3 | 0.33333 | 0.33333 |

2 | 1/3 | 0.66667 | 1.33333 |

3 | 1/3 | 1.00000 | 3.00000 |

total | 2.0000 | 4.6667 | |

E(x) =μ= | ΣxP(x) = | 2.0000 | |

E(x^{2}) = |
Σx^{2}P(x) = |
4.6667 | |

Var(x)=σ^{2} = |
E(x^{2})-(E(x))^{2}= |
0.6667 | |

std deviation= |
σ= √σ^{2} = |
0.8165 |

since n=35 is greater than 30 , we can use normal approximation:

for normal distribution z score =(X-μ)/σ | |

here mean= μ= | 2 |

std deviation =σ= | 0.817 |

sample size =n= | 35 |

std error=σ_{x̅}=σ/√n= |
0.1380 |

probability
=P(2.1<X<2.6)=P((2.1-2)/0.138)<Z<(2.6-2)/0.138)=P(0.72<Z<4.35)=1-0.7642=0.2358 |

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Subscript ij right bracketA=Aij if A is 2*3 and
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(b) Construct the 2*4 matrix Upper C equals left bracket left
parenthesis 3 i plus j right parenthesis squared right
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2.
Solve the following matrix equation.
left bracket Start 2 By 2 Matrix 1st Row 1st Column 3 x 2nd
Column 4 y minus 5 2nd Row...

Question 2
Suppose that X has a discrete uniform distribution
f(x)={1/3, x=1,2,3
0, otherwise
A random sample of n=37 is selected from this population. Find
the probability that the sample mean is greater than 2.1 but less
than 2.4.
Express the final answer to four decimal places (e.g.
0.9876).
The probability is ???

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A proton moves through a uniform magnetic field given by
ModifyingAbove Upper B With right-arrow equals left-parenthesis
10.5ModifyingAbove i With caret minus 21.6ModifyingAbove j With
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