Question

The weight of topsoil sold in a week is normally distributed with a mean of 1200 tons and a standard deviation of 24 tons.

(a) What percentage of weeks will sales exceed 1212 tons? (Round your answer to two decimal places.)
%

(b) What percentage of weeks will sales be less than 1164 tons? (Round your answer to two decimal places.)
%

(c) What percentage of weeks will sales be between 1188 and 1212 tons? (Round your answer to two decimal places.)
%

Answer 1

Solution :

(a)

P(x > 1212) = 1 - P(x < 1212)

= 1 - P[(x - ) / < (1212 - 1200) / 24)

= 1 - P(z < 0.5)

= 1 - 0.6915

= 0.3085

percentage = 30.85%

(b)

P(x < 1164) = P[(x - ) / < (1164 - 1200) / 24]

= P(z < -1.5)

= 0.0668

percentage = 6.68%

(c)

P(1188 < x < 1212) = P[(1188 - 1200)/ 24) < (x - ) /  < (1212 - 1200) / 24) ]

= P(-0.5 < z < 0.5)

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

= 0.6915 - 0.3085

= 0.383

percentage = 38.30%