Question

In: Statistics and Probability

A sample of n=23 observations is drawn from a normal population with μ=1030 and σ=210. Find...

A sample of n=23 observations is drawn from a normal population with μ=1030 and σ=210. Find each of the following:

A. P(X¯>1117)

Probability =

B. P(X¯<964)

Probability =

C. P(X¯>1012)

Probability =

Solutions

Expert Solution

Solution :

Given that ,

mean = = 1030

standard deviation = = 210

= / n = 210 / 23 = 43.7880

A.

P( > 1117) = 1 - P( < 1117)

= 1 - P[( - ) / < (1117 - 1030) / 43.7880]

= 1 - P(z < 1.99)

= 1 - 0.9767

= 0.0233

Probability = 0.0233

B.

P(x 964)

= P[(x - ) / (964 - 1030) / 43.7880]

= P(z -1.51)

= 0.0655

Probability = 0.0655

C.

P( > 1012) = 1 - P( < 1012)

= 1 - P[( - ) / < (1012 - 1030) / 43.7880]

= 1 - P(z < -0.41)

= 1 - 0.3409

= 0.6591

Probability = 0.6591

orchestra answered 3 years ago
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