Question

a.) The shelf life of Energized AA batteries is normally distributed, with a mean of 10 years and a standard deviation of 0.1 years. What is the value of the shelf life for the first quartile?

b.) The time it takes Professor Smith the grade a single midterm exam is normally distributed with a mean of 5 minutes and a standard deviation of 1.7 minutes. If there are 60 students in her class, what is the probability it will take her longer than 5 hours to grade all of the midterm exams?

Answer 1

Solution:-

Given that,

mean = = 10

standard deviation = =0.1

Using standard normal table,

The z dist'n First quartile is,

P(Z < z) = 25%

= P(Z < z) = 0.25  

= P(Z < -0.6745 ) = 0.25

z = -0.6745

Using z-score formula,

x = z * +

x = -0.6745 * 0.1+10

x = 9.93255

First quartile =Q1 = 9.93255

(b)

Solution :

Given that ,

mean = = 5

standard deviation = =1.7

n = 60

= 5

= / n = 1.7 / 60 = 0.2195

x=5 hr=300 minutes

P( > 300) = 1 - P( <300 )

= 1 - P[( - ) / < ()300 -5 /0.2195 ]

= 1 - P(z < 1343.96)

Using z table

= 1 - 1

= 1

probability= 1