Question

In: Statistics and Probability

Suppose a simple random sample of size n=36 is obtained from a population with μ=81and σ=24....

Suppose a simple random sample of size n=36 is obtained from a population with μ=81and σ=24.

(a) Describe the sampling distribution of barx (mean and standad deviation).

(b) What is P (barx>85)?

(c) What is P (barx≤71)?

(d) What P (75.8<barx<90.6)?

Expert Solution

Solution :

Given that ,

a) = 81

= / n = 24 / 36 = 4

b) P( > 85) = 1 - P( < 85)

= 1 - P[( - ) / < (85 - 81) / 4]

= 1 - P(z < 1.0)

= 1 - 0.8413

= 0.1587

c) P( 71) = P(( - ) / (71 - 81) / 4)

= P(z -2.50 )

Using z table

= 0.0062

d) P( 75.8 < < 90.6)

= P[(75.8 - 81) / 4 < ( - ) / < (90.6 - 81) / 4 )]

= P(-1.30 < Z < 2.40)

= P(Z < 2.40) - P(Z < -1.30)

Using z table,

= 0.9918 - 0.0968

= 0.8950

orchestra answered 2 years ago

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