Question

Suppose the longevity of iPad batteries can be modeled by a normal distribution with mean μ = 8.2 hours and standard deviation σ = 1.2 hours.

a. Find the probability a randomly selected iPad lasts less than 10 hours.

b. Find the 25th percentile of the battery times.

Answer 1

Solution :

Given that,

mean = = 8.2

standard deviation = = 1.2

P(X<10 ) = P[(X- ) / < (10-8.2) /1.2 ]

= P(z <1.5 )

Using z table

=0.9332

probability=0.9332

(B)

Using standard normal table,

P(Z < z) = 25%

= P(Z < z) = 0.25  

= P(Z <- 0.67 ) = 0.25

z = -0.67 Using standard normal z table,

Using z-score formula  

x= z * +

x= - 0.67 *1.2+8.2

x= 7.396