Problem #2: The weight of a sophisticated running shoe is normally distributed w

Question

Problem #2: The weight of a sophisticated running shoe is normally distributed with a mean of 13 ounces (a) What must the standard deviation of weight be in order for the company to state that 95% of its shoes weight less than 14 ounces? (b) Suppose that the standard deviation is actually 0.84. If we sample 8 such running shoes, find the probability that exactly 4 of those shoes weigh more than 14 ounces Problem #2(a): Problem #2(b): Just Save Submit Problem #2 for Grading Attempt #3 2(a) 2(b) 2(a) 2(b) Problem #2 Attempt #2 2(a) 2 (a) Attempt #1 Your Answer: 2(a) 2(b) Your Mark: 2(a) 2(b) t)

Explanation / Answer

Ans:

Given that

mean=13

z=(x-mean)/std. dev

a)P(Z<z)=0.95

z=1.645

1.645=(14-13)/std dev.

1.645=1/std dev.

std. dev=1/1.645=0.608

standard deviation=0.608

b)

z=(14-13)/0.84=1.19

P(z>1.19)=1-P(z<=1.19)=1-0.8830=0.1170

Now use binomial distribution:

n=8,p=0.117

P(k=4)=8C4*0.1174*0.8834=0.0080

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