Question

Suppose the lengths of bread made at a bakery is distributed normally with a mean of 20 cm and standard deviation of 3.5 cm.

a. What is the probability that a single randomly selected bread has a length less than 22 cm?

b. what is the probability the mean length of 12 randomly selected breads is less than 22 cm?

Answer 1

Solution :

(a)

P(x < 22) = P[(x - ) / < (22 - 20) / 3.5]

= P(z < 0.57)

= 0.7157

(b)

= / n = 3.5 / 12

P( < 22) = P(( - ) / < (22 - 20) / 3.5 / 12 )

= P(z < 1.98)

= 0.9761