Math 問題 probability HELP ME>O<

2012-10-25 2:49 am

A soft-drink machine is regulated so that it discharges an average of 200 milliliters per cup. If the amount of drink is normally distributed with a standard deviation equal to 15 milliliters,

a. what fraction of the cups will contain more than 224 milliliters?

b. what is the probability that a cup contains between 191 and 209 milliliters?

c. how many cups will probably overflow if 230 milliliter cups are used for the next 1000 drinks?

d. below what value do we get the smallest 25% of the drinks?

回答 (1)

myisland8132

2012-10-25 5:38 am

✔ 最佳答案

Let X be the amount of drink

(a) P(X > 224)

= P(Z > (224 - 200)/15)

= P(Z > 1.6)

= 0.0548

(b) P(191 <= X <= 209)

= P(-0.6 <= X <= 0.6)

= 0.4515

(c) P(X > 230)

= P(Z > 2)

= 0.02275

So, there will be 22 or 23 cups overflow

(d) P(Z <= -0.6745) = 0.25 (using software or Z - table)

So, the value is 200 - 15 * 0.6745 = 189.9 mL

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