A specialist coffee machine dispenses espresso shots and steamed milk. The volume of an espresso shot, EEE ml, is normally distributed such that E∼N(35,2.52)E \sim N(35, 2.5^2)E∼N(35,2.52).
Four espresso shots are selected at random.
Find the probability that their total volume exceeds 146.5 ml.
The volume of a portion of steamed milk, MMM ml, is normally distributed such that M∼N(150,62)M \sim N(150, 6^2)M∼N(150,62).
Two espresso shots and three portions of milk are selected at random.
Find the probability that the total volume of these five components is less than 500 ml.
A random sample of nnn portions of milk M1,M2,…,MnM_1, M_2, \dots, M_nM1,M2,…,Mn is taken. A new random variable VVV is defined by the espresso machine's calibration offset:
V=(n−1)M1−∑r=2nMr V = (n-1)M_1 - \sum_{r=2}^{n} M_r V=(n−1)M1−r=2∑nMrGiven that P(V>41.57)=0.0228P(V > 41.57) = 0.0228P(V>41.57)=0.0228 correct to 4 decimal places,
determine the value of nnn.
