Sections 5.3&5.4 2. [21 points] Suppose that 10-ft lengths of a certain type of

Question

Sections 5.3&5.4 2. [21 points] Suppose that 10-ft lengths of a certain type of cable have breaking strengths that are normally distributed with mean 450 lb and standard deviation 50 lb Find the probability that one such cable will have a strength greater than 536 lb. [4 points] / Let X = the mean breaking strength for a random sample of nine such cables. Clearly, the value of X will vary from one sample to another. Describe its sampling distribution by giving the (G) shape, (ii) mean, and (ii) standard deviation of the distribution. [1 point each] Find the probability that the sample mean of nine cables will be between 423 and 48o. [4 points] (d) Find the probability that the sample mean of 35 cables will be less than 428. [4 points] (e) Suppose that the distribution of breaking strengths for all cables in the population had been non-normal or unknown. [2 points each] (i) Could part (a) have been solved using the information given? Why or why not? (ii) Could part (c) have been solved using the information given? Why or why not? ii) Could part (d) have been solved using the information given? Why or why not? 20 points] Suppose that the weights of people who work in an office building are normally distributed with a mean of -165 lb and a standard deviation of 25 lb. [4 points each] (a) What is the probability that one person, selected at random from the building, weighs (b) Suppose that three people are selected independently of each other. Find the probability (c) Find the probability that a sample of three people will have a mean weight greater than (d) What is the conceptual difference between parts (b) and (c), i.e. how are the events (e) Have you ever ridden in an elevator and read a sign stating its maximum more than 200 lb? that all three weigh more than 200 lb, i.e. find P(X, >200 200 lb different? X, >200x, > 200). oad and wondered about the chances the elevator would be overloaded? What is the chance that the total weight of five people is more than 1000 Ib, i.e. what is P(x, +...tx, > 1000)? Hint - try to re-express this as an X-style problem.

Explanation / Answer

SolA:

mean=450

sd=50

P(X>536)

z=x-mean/sd

=536-450/50

=1.72

P(Z>1.72)

=1-P(z<1.72)

=1-0.9573

=0.0427

solutiion:

shape bell curve

mean=450

sd=50/sqrt(9)

=50/3

=16.67

solutionc:

n=9

P(423<X<480)

=423-450/50/sqrt(9)<z<480-450/50/sqrt(9)

=P(-1.62<z<1.8)

=P(Z<1.8)-P(Z<-1.62)

=0.9641-(1-0.9474)

=0.9115

ANSWER:0.9115

SOLUTIOND:

n=35

P(X<428)

P(Z<428-450/50/sqrt(35)

=P(Z<-2.603)

=1-P(Z<2.603)

=1-0.9953

=0.0047

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