Question

A normal random variable x has mean μ = 1.8 and standard deviation σ = 0.18. Find the probabilities of these X-values. (Round your answers to four decimal places.)

(a)    

1.00 < X < 1.50

(b)    

X > 1.39

(c)    

1.45 < X < 1.60

Answer 1

a)

Solution :

Given that ,

mean =   = 1.8

standard deviation = = 0.18   

P(1.00< x < 1.50) = P[(1.00-1.8) /0.18 < (x - ) / < (1.50-1.8) / 0.18)]

= P(-4.44 < Z < -1.67)

= P(Z < -1.67) - P(Z < -4.44)

Using z table   

= 0.0475 - 0

probability= 0.0475

b)

P(x >1.39 ) = 1 - P(x< 1.39)

= 1 - P[ X - / / (1.39-1.8) /0.18 ]

= 1 - P(z <-2.28 )

Using z table

= 1 - 0.0113

= 0.9887

probability= 0.9887

c)

P(1.45< x < 1.60) = P[(1.45-1.8) / 0.18< (x - ) / < (1.60-1.8) /018 )]

= P(-1.94 < Z < -1.11)

= P(Z < -1.11) - P(Z < -1.94)

Using z table   

= 0.1335 -0.0262

probability= 0.1073