Question

. The lifetimes of bateries sold by company x are normaly distributed, with mean 150 hours and standard deviation 25 hours. A box contains 12 batteries from company X (a) Find the expected number of these batteries that have a lifetime of more than 160 hours. The lifetimes of batteries sold by company Y are normally distributed, with mean 160 hours and 80% of these batteries have a lifetime of less than 180 hours. (b) Find the standard deviation of the lifetimes of batteries from company Y Both companies sell their batteries for the same price. (c) State which company you would recommend. Give reasons for your answer

Answer 1

Lifetimes 여 battery sold by compar- are nonmallq distui bu Compan tor σ 25 hours (a) Eypected number these ba廾eties that haue a ufetimes of more tan 160 houns - n -PX160 - 121- 16-159 29厄 12 (1386) = 12 [t-o.IF Company y are (b) 녀etimes oj batteries sold tづ normally dist外buted with and 80% 어 hose 160hours these batfevies haue a lifetime less than 13o houns Using cumulotiwe sfand sin cumotative s tandand noma dlistbution tob e 0.84 2

o. 84 180 160 -23.81 o, 84 TUwevid srecomnend compars becavse The lifetimes bofterier sold Corpa"J у l's JX.oaten than that Of com t of Compan