Question

For a normal distribution where μ = 100 and σ = 10, what is the probability of:
1. P (X> 80) =
2. P (95 <X <105) =
3. P (X <50) =
4. P (X <100) =
5. P (X <90 and X> 110) =
6.P (X> 150) =

Answer 1

Solution :

Given that ,

mean = = 100

standard deviation = = 10

(1)

P(x > 80) = 1 - P(x < 80)

= 1 - P[(x - ) / < (80 - 100) / 10]

= 1 - P(z < -2)

= 0.9772

(2)

P(95 < x < 105) = P[(95 - 100)/ 10) < (x - ) /  < (105 - 100) / 10) ]

= P(-0.5 < z < 0.5)

= P(z < 0.5) - P(z < -0.5)

= 0.3829

(3)

P(x < 50) = P[(x - ) / < (50 - 100) / 10]

= P(z < -5)

= 0

(4)

P(x < 100) = P[(x - ) / < (100 - 100) / 10]

= P(z < 0)

= 0.5

(5)

1 - P[(90 - 100)/ 10) < (x - ) /  < (110 - 100) / 10) ]

= 1 - P(-1 < z < 1)

= 0.3173

(6)

P(x > 150) = 1 - P(x < 150)

= 1 - P[(x - ) / < (150 - 100) / 10]

= 1 - P(z < 5)

= 0