Question

Organic tomatoes weighs 75 grams but 10% of the tomatoes are too small. It is reasonable to say the mean weight is 75 grams with a standard deviation of 5 grams.

A) What is the probability that the tomato yield exceeds 85 grams for all organic farms?

B) 1% of tomatoes would weigh higher than ___ ?

Answer 1

Solution :

Given that ,

mean = = 75

standard deviation = = 5

a) P(x > 85 ) = 1 - p( x< 85)

=1- p P[(x - ) / < (85 -75) / 5]

=1- P(z < 2 )

Using z table,

= 1 - 0.9772

= 0.0228

b) Using standard normal table,

P(Z > z) = 1 %

= 1 - P(Z < z) = 0.01  

= P(Z < z) = 1 - 0. 01

= P(Z < z ) = 0.99

= P(Z < 2.326 ) = 0. 99

z = 2.326

Using z-score formula,

x = z * +

x = 2.326 * 5 + 75

x = 86.63