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)

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 2 years ago

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