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# [20點] 關於probability的問題

1) The scores of a English test taken by 400 students are normally distributed with a mean of 60 and standard deviation of 10. The passing mark of the test is 40

i) How many students scored more than 80?

II) What is the probability that is a randomly chosen student failed in the test?

2) It is known that 10% of the appliances produced by a production plant are defective. Five of those appliances are going through QC inspections.

i) What is the probability that 4 out of the 5 appliances are defective?

ii) What is the probability that at least one og the 5 appliances is/are defective?

### 1 Answer

- AdamLv 79 years agoFavorite Answer
1.

The normal table :

http://www.sjsu.edu/faculty/gerstman/EpiInfo/z-tab...

i)

P(x > 80)

= P(z > (80 - 60)/10)

= P(z > 2)

= 1 - P(z ≤ 2)

= 1 - 0.9772

= 0.0288

ii)

P(x < 40)

= P(z < (40 - 60)/10)

= P(z < -2)

= P(z > 2)

= 0.0288

= = = = =

2)

i)

P(4 out of 5 appliances are defective)

= C(5, 4) ´ (10%)^4 ´ (1 - 10%)

= 5 ´ (0.1)^4 ´ 0.9

= 0.00045

ii)

P(at least one of the 5 appliances is defective)

= 1 - P(none of the 5 appliances is defective)

= 1 - (1 - 10%)^5

= 0.40951

Source(s): Adam