Question

Please show work on the one I write "I need this most" I already answered i-iv

Teacher gave these answers Answers:-0.9; 192; .8159; .1151; 142.4; .43, 176.6

1. You are given that the distribution of the weights of male adults has normal distribution with mean μ = 168 lbs and standard deviation σ = 20 lbs. Answer the following questions:

i) If John has weight of 150 lbs, what is the z-score of John’s weight?

(ii) If Peter’s weight is 1.2 σ above the mean, what is Peter’s weight?

(iii) What is the probability that a randomly chosen male adult is heavier than John?

(iv) What is the probability that a randomly chosen male adult is heavier than Peter?

(v) Jack is small, only 10% of the male adults are lighter than Jack. What is the z-score of Jack’s weights? How much does Jack weigh? (I need this most)

(Vi) Dan is a big guy; he is heavier than two-thirds of the male adults. Find the z-score of Dan’s weight and Dan’s actual weight. (I need this most)

Answer 1

(v)

Here we need z-score that have 0.10 area to its left. The z-score -1.28 has 0.10 area its left.

The Jack's weight will be

Answers:

The z-score of Jack’s weights : -1.28

Jack weight = 142.4

(vi)

Heavier than two third of male means heavier than 0.67 males. Here we need z-score that has 0.6667 area to its left. The z-score 0.44 has 0.67 area to its left. So Dan’s actual weight is

Answers:

The z-score of Dan’s weight : 0.43

Dan’s actual weight = 176.6