Let X equal the weight of a cookie. Assume that the distribution of X is N(14.22,0.0854). These cookies are sold in packages with labeled weight 340. The number of cookies is usually 24, 25, or 26. Assuming that the package is filled with a random sample of cookies, how many cookies should be put into a package to be quite certain (say with probability of at least .95) that the total weight of the cookies exceeds 340? (Extra cookies decreases profit.)

Please show all work when calculating means, variances, and z-scores(? the number you look up on the table to get the probability.)

2. Originally Posted by JJMC89
Let X equal the weight of a cookie. Assume that the distribution of X is N(14.22,0.0854). These cookies are sold in packages with labeled weight 340. The number of cookies is usually 24, 25, or 26. Assuming that the package is filled with a random sample of cookies, how many cookies should be put into a package to be quite certain (say with probability of at least .95) that the total weight of the cookies exceeds 340? (Extra cookies decreases profit.)

Please show all work when calculating means, variances, and z-scores(? the number you look up on the table to get the probability.)
Let Y = X1 + X2 + X3 + .... + Xn.

Y ~ Normal(mean = 14.22n, variance = 0.0854n)

You require Pr(Y > 340) = 0.95. In other words:

z* = (340 - 14.22n)/sqrt{0.0854n} where Pr(Z > z*) = 0.95.

Get z* from tables. Substitute and solve for n.

3. n = 25