Question

Given that X is normally distributed with μ = 304.6 and σ = 13.2, find the probability that X is less than 310.5, given that we know that X is larger than 288.4. State your answer rounded to 3 places of decimal.

Your Answer:

Answer 1

Solution :

Given that ,

mean = = 304.6

standard deviation = = 13.2

P(X<310.5 ) = P[(X- ) / < (310.5 - 304.6) /13.2 ]

= P(z < 0.45)

Using z table

= 0.6736

probability=0.674

(B)

P(x >288.4 ) = 1 - P(x<288.4 )

= 1 - P[(x -) / < (288.4 -304.6) / 13.2]

= 1 - P(z < -1.23)

Using z table

= 1 - 0.1093

= 0.8907

probability= 0.891