Use the following information to answer problems 1 through 7 below: Assume that

Question

Use the following information to answer problems 1 through 7 below: Assume that in a large population of white pine trees (Pinus strobus, anillinious native), the lengths of falle mature seed cones are normally distributed with meu = 15.4 cm and sigma = 4.5 cm, then: If one such cone is randomly selected, what is the probability that it will be between 10.9 cm and 19.9 cm long? (no continuity correction) If a sample of three cones is randomly chosen, what is the probability that the sample average cone length will be between 14 cm and 16 cm long? (no continuity correction) If a sample of five cones is randomly chosen, what is the probability that the sample average cone length will be between 14 cm and 16 cm long? (no continuity correction) Repeat problem #2 but now use the continuity correction; unit of measurement = 1.0 cm. Repeat problem #2 but now the continuity correction; unit of measurement = 0.5 cm. Repeat problem #3 but now use the continuity correction; unit of measurement = 0.5 cm. Repeat problem #3 but now the continuity correction; unit of measurement = 0.25 cm.

Explanation / Answer

There are multiple questions. Two questions answered

1).

Z value for 10.9, z=(10.9-15.4)/4.5 = -1

Z value for 19.9, z=(19.9-15.4)/4.5 = 1

P( 10.9<x<19.9) = P( -1<z<1)

P( z <1) – P( z< -1)

= 0.8413 - 0.1587

= 0.6826

2)

Standard error =sd /sqrt(n) =4.5/sqrt(3) =2.5981

Z value for 14, z=(14-15.4)/2.5981 = -0.54

Z value for 16, z=(16-15.4)/2.5981 = 0.23

P( 14<x<16)=P( -0.54<z<0.23)

P( z <0.23) – P( z < -0.54)

= 0.591 - 0.2946

=0.2964

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