# Statistics 統計學問題

Q1. The probabilities that a batch of 4 computers will contain 0,1,2,3 and 4 defective computers are 0.5729, 0.0767, 0.0076, and 0.0003, respectively. Find the variance of the probability distribution.

Q2. The mean is u=137.0 and the standard deviation is o=5.3. Find the probability that X is between 134.4 and 140.1.

( Assume that X has a normal distribution, and find the indicated probability.)

Q3. A history teacher assigns letter grades on a test according to the following scheme.

A: Top 10%

B: Scores below the top 10% and above the bottom 60%

C: Scores below the top 40% and above the bottom 20%

D: Scores below the top 80% and above the bottom 10%

F: Bottom 10%

Scores on the test are normally distributed with a mean of 70 and a standard deviation of 12.6. Find the numerical limits for each letter grade.

Q4. Determine whether the given procedure results in a binomial distribution. If not, state the reason why.

Choosing 4 marbles from a box of 40 marbles ( 20 purple, 12 red, and 8 green) on a time without replacement, keeping track of the number of red marbles chosen.

Can someone help me to solve those problems?

Thanks

### 1 個解答

• 最佳解答

Q1. The probabilities that a batch of 4 computers will contain 0,1,2,3 and 4 defective computers are 0.5729, 0.0767, 0.0076, and 0.0003, respectively. Find the variance of the probability distribution.

在一批4台電腦裡會包含0, 1,2,3,以及4台有缺陷的電腦的機率個別是0.5729, 0.0767, 0.0076以及0.0003. 請找出機率分佈的變異數(variance)

(0,1,2,3, and 4共五種可能, 但機率只有0.5729, 0.0767, 0.0076, and 0.0003四種, 是不是漏了一個????????)

Q2. The mean is u=137.0 and the standard deviation is o=5.3. Find the probability that X is between 134.4 and 140.1.

( Assume that X has a normal distribution, and find the probability.)

u的平均值=137.0, 標準差 o = 5.3, 請找出X落於134.4與140.1之間的機率是多少?(假設X是正常的分佈, 請找出其機率)

Q3. A history teacher assigns letter grades on a test according to the following scheme.

A: Top 10%

B: Scores below the top 10% and above the bottom 60%

C: Scores below the top 40% and above the bottom 20%

D: Scores below the top 80% and above the bottom 10%

F: Bottom 10%

Scores on the test are normally distributed with a mean of 70 and a standard deviation of 12.6. Find the numerical limits for each letter grade.

一位歷史老師在一次測驗中根據以下的分類表來指定字母的等級(即A, B, C, D,…等級)

A: 前10%,

B:分數低於前10%而大於後面算來60%(介於前10%~40%的意思)

C: 分數低於前40%而大於後面算來20%(介於前40%~80%的意思)

D: 分數低於前80%而大於後面算來10%(介於前80%~90%的意思)

F: 倒數10%

分數在這次測驗是屬於正常分佈, 平均值為70, 標準差為12.6, 請找出

每一個字母等級的數值的限制(就是算出各字母等級所佔人數的百分比)

Q4. Determine whether the given procedure results in a binomial distribution. If not, state the reason why.

Choosing 4 marbles from a box of 40 marbles ( 20 purple, 12 red, and 8 green) on a time without replacement, keeping track of the number of red marbles chosen.

決定是否所給與的步驟會產生兩項式的分佈(binomial distribution), 如果不會請說明原因為何?

從一個有40顆寶石的盒子(紫色20顆, 紅色12顆, 綠色8顆)裡一次選4顆寶石,

在不更換的情況之下, 記錄選到紅色大理石的數量>

Can someone help me to solve those problems?

Thanks

有誰可以幫我解這些問題嗎? 謝謝!