(6) The battery lives for the Hoverboard 360 are normally distributed with a mea

Question

(6) The battery lives for the Hoverboard 360 are normally distributed with a mean of 124 days and a standard deviation of g days (a) Batteries that last under 110 days are considerad defective Find the proportion of defective (2 pts) Ho e board 360 batteries notation llustrate the probability with a picture and use correct probability 10 b) In a customer sat sfaction survey, a sample of 144 Haverboard 360 customers were asked: (4 pts) Does your battery last cver 110 days betore needing to be recherged?" Describe the distribution of proportion of customers in the sample who answer no" to this question. Include the values of any parameters of the distribution. Justify your answer (129,.5) V (PJI (c) Find the probabilty that, in a sample of L1 batteries died in under 110 days is at least 0.03. Ilustrate this quanity with a picture as well as use correct probability notation. customers the proportion of customers whose (2 pts) (x132)

Explanation / Answer

Question 1(b)

Here the distribution of proportion of customers in the sample who answer "No" to this question is binomial distribution where

n = 144

and

p = 0.06 (as calculated in previous question)

it can be approximated by normal approximation where

BIN (n = 144 ; p = 0.06) ~ NORM (0.06, 0.0198)

Here we have to find

Pr(p^ >= 0.03) = 1 - NORM(p^ < 0.03 ; 0.06 ; 0.0198)

Z = (0.03 - 0.06)/0.0198 = -1.5159

Pr(p^ >= 0.03) = 1 - NORM(p^ < 0.03 ; 0.06 ; 0.0198) = 1 - Pr(Z < -1.5159)

= 1 - 0.0648 = 0.9352

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