Question

​1) X is normally distributed with a mean of 60 and a standard deviation of 12.

​​a) Find the probability that X is less than 42

​​b) Find the probability that X is more than 70.

​2) Weights of Yellow Labradors are normally distributed with a mean of 55 pounds and a standard

​​deviation of 6.2 pounds. What proportion of Yellow Labradors weigh between 50 and 60 pounds?

Answer 1

Solution :

1) Given that ,

a) P(x < 42)

= P[(x - ) / < (42 - 60) / 12]

= P(z < -1.50)

Using z table,

= 0.0668

b) P(x > 70) = 1 - p( x< 70)

=1- p P[(x - ) / < (70 - 60) / 12 ]

=1- P(z < 0.83 )

= 1 - 0.7967

= 0.2033

2) Given that ,

mean = = 55

standard deviation = = 6.2

P(50 < x < 60) = P[(50 - 55)/ 6.2) < (x - ) /  < (60 - 55) / 6.2) ]

= P(-0.81 < z < 0.81)

= P(z < 0.81) - P(z < -0.81)

Using z table,

= 0.7910 - 0.2090

= 0.5820