Question

Suppose the size of lobsters caught in the US on any given day are normally distributed, with a mean of 36 ounces and a standard deviation of 5 ounces. What is the P[X < 20], P[28 < X < 40], and P[ X > 42]?

Answer 1

Solution :

Given that ,

mean = = 36

standard deviation = = 5

P(x < 20) = P((x - ) / < (20 - 36) / 5)

= P(z < -3.2)

= 0.0007

P[X < 20] = 0.0007

P(28 < x < 40) = P((28 - 36)/ 5) < (x - ) / < (40 - 36) / 5) )

= P(-1.6 < z < 0.8)

= P(z < 0.8) - P(z < -1.6)

= 0.7881 - 0.0548

= 0.7333

P[28 < X < 40] = 0.7333

P(x > 42) = 1 - P(x < 42)

= 1 - P((x - ) / < (42 - 36) / 5)

= 1 - P(z < 1.2)

= 1 - 0.8849

= 0.1151

P[ X > 42] = 0.1151