Question

A pontoon on granite in a park has maximum weight of 12 people or 1776 Ib . if mean weight for men is 172 Ib each standard deviation of 29 Ib.

a)find the probability if an individual man is randomly selected, his weight will be greater than 148 Ib.

b)Find the probability that 8 random selected men will have mean greater than 222Ib( hence total weight exceeds the maximum capacity pontoon

Answer 1

ANSWER:

Given data,

A pontoon on granite in a park has maximum weight of 12 people or 1776 Ib . if mean weight for men is 172 Ib each standard deviation of 29 Ib.

Mean = = 172

Standard deviation = = 29

a) find the probability if an individual man is randomly selected, his weight will be greater than 148 Ib.

P(x > 148) = P((x-)/ > (148-172)/29)

P(x > 148) = P(z > -24/29)

P(x > 148) = P(z > -0.83)

P(x > 148) = 1 - P(z < -0.83)

P(x > 148) = 1 - 0.20327 (From z score table as given below)

P(x > 148) = 0.79673

P(x > 148) = 0.79673 (Rounded to four decimal places)

b) Find the probability that 8 random selected men will have mean greater than 222 Ib ( hence total weight exceeds the maximum capacity pontoon.

P(x > 222) = P((x-)/(/sqrt(n)) > (148-172)/(29/sqrt(8)))

P(x > 222) = P(z > -24/(29/sqrt(8)))

P(x > 222) = P(z > -2.34)

P(x > 222) = 1 - P(z < -2.34)

P(x > 222) = 1 - 0.00964 (From z score table as given below)

P(x > 222) = 0.99036

P(x > 222) = 0.9904 (Rounded to four decimal places)

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