Question 7. The Prototype Shoe The weight of a sophisticated running shoe is nor

Question

Question 7. The Prototype Shoe The weight of a sophisticated running shoe is normally distributed with a mean of 10 ounces and a standard deviation of 0.7 ounce ?? ? (a) What is the probability that a shoe weighs more than 13 ounces? (b) What must the standard deviation of weights be in order for the company to state that, 99% of its shoes weighs less than 13 ounces? (c) If the standard deviation remains at 0.7 ounce, what must the mean weight be for th company to state that 99% of its shoes weighs less than 13 ounces?

Explanation / Answer

mean = 10 ,s = 0.7

a)
P(x >13)
z = (x -mean)/s
= ( 13 - 10)/ 0.7
= 4.2857

P(x >13) = P(z > 4.2857)= 0 by suing z standard table

b)

z value at 99% = 2.576

z = ( x -mean) /s

2.326 = ( 13 - 10) /s
s = 1.2898

c)

std.dev = 0.7 , z value at 99% = 2.326
z = ( x -mean) /s

2.326 = ( 13 - mean) /0.7
mean = 11.3718

  

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.