3) Rockingham Corporation makes electrical shavers. The life (period during whic

Question

3) Rockingham Corporation makes electrical shavers. The life (period during which a shaver does not need major repair) of a Model J55 manufactured by this corporation has a normal distribution with a mean of 70 months and a standard deviation of 8 months a) What is the probability that a randomly selected shaver of this model has life time at months? least 65 b) What percent of shavers of this kind will have life time between 60 and 77 months? c) Any shaver that needs a major repair during the warranty period will be replaced free by the company. What should be the warranty period if the company does not want to replace more than 3% of the shavers? 4) The lifetime of a certain type of battery is normally distributed with a mean of 10 hours and a standard deviation of 1.5 hours. There are 4 batteries in a package. a) What is the probability that the mean life time of the package is exceeds 11 hours?

Explanation / Answer

Solution:-
3) Given that mean = 70 , sd = 8
a) P(X >= 65) = P(Z >= (X - )/
= P(Z >= (65 - 70)/8)
= P(Z >= -0.625)
= 0.7357

b) P(60 < X < 77) = P((X - )/ < Z < (X - )/)
= P((60 - 70)/8 < Z < (77 - 70)/8)
= P(-1.25 < Z < 0.875)
= 0.705

c) P(X <= x) = 0.03
(X - 70)/8 = -1.8808
X = 70 - 1.8808*8
X = 54.9536

4) Given mean = 10 sd = 1.5 n = 4
P(x > 11) = P( Z > (X - )/(/sqrt(n)))
= P( Z > (11 - 10)/(1.5/sqrt(4)))
= P( Z > 1.3333)
= 0.0918

  

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

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