Question

(A) The amount of tea leaves in a can from a particular production line is normally distributed with μ (mean) = 110 grams and σ (Standard deviation) = 5 grams.

(i) What is the probability that a randomly selected can will contain less than 105 grams of tea leaves?                           

(ii) If a sample of 9 cans is selected, what is the probability that the sample mean of the content “tea leaves” to be more than 115 grams?           

(B) In a city, it is estimated that the maximum temperature in July is normally distributed with a mean of 23º and a standard deviation of 4°. Calculate the probability of having a maximum temperature between 20° and 28°                                                 

Answer 1

Solution :

(A)

(i)

P(x < 105) = P[(x - ) / < (105 - 110) / 5]

= P(z < -1)

= 0.1587

Probability = 0.1587

(ii)

= / n = 5 / 9 = 1.6667

P( > 115) = 1 - P( < 115)

= 1 - P[( - ) / < (115 - 110) / 1.6667]

= 1 - P(z < 3.00)

= 1 - 0.9987

= 0.0013

Probability = 0.0013

(B)

P(20 < x < 28) = P[(20 - 23)/ 4) < (x - ) /  < (28 - 23) / 4) ]

= P(-0.75 < z < 1.25)

= P(z < 1.25) - P(z < -0.75)

= 0.8944 - 0.2266

= 0.6678

Probability = 0.6678