**Please answer both questions** Question #1: Two parts Question #2: Two parts F

Question

**Please answer both questions**
Question #1: Two parts
Question #2: Two parts

Find z such that 8.6% of the standard normal curve lies to the right of Z. Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 28 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 7 months, and the distribution of lifetimes is normal. If Accrotime guarantees a full refund on any defective watch for 2 years after purchase, what percentage of total production will the company expect to replace? (answer to two decimal places.) (b) If Accrotime does not want to make refunds on more than 13% of the watches it makes, how long should the guarantee period be (to the nearest month)?

Explanation / Answer

1)

area to the right of z is 8.6% of the total area

corresponding diagram in the above question is second option

P(Z >z) = 0.086

=>

z = invnorm(1 - 0.086) = 1.366

2)

a)

P(X < 24) = P(Z <24-28/7)

= P(Z < -0.5714)

= 0.2839

b)

P(X < x) = 0.13

=>

x-28/7 = invnorm(0.13) = -1.126

x = 20.118

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