# 請問 organisms,的意思

Biology as a separate science was developed in the nineteenth century as scientists discovered that organisms shared fundamental characteristics. Biology is now a standard subject of instruction at schools and universities around the world, and over a million papers are published annually in a wide array of biology and medicine journals.

1. 由此常態母體中抽出 n=4 的隨機樣品：

(a) P( <2.5)=?

(b) P( >Y)=0.03 的Y=?

2. 由此常態母體中抽出 n=15 的隨機樣品：

(c) P(2.8 < <3.8)=?

(d) P(Y< <3)=0.17的Y=?

1. 某位學生的分數是高於510的機率為何? 低於400?

2. 若隨機抽出16位學生，求他們的平均分數( )介於480到520的機率為何?

3. 以500為中心, 有90%的機率此16名樣本的平均分數會介於多少之間?

4. 有80%的機率此16名樣本的平均分數會高於多少?

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Most biological sciences are specialized disciplines. Traditionally, they are grouped by the type of organism being studied: botany, the study of plants; zoology, the study of animals; and microbiology, the study of microorganisms. The fields within biology are further divided based on the scale at which organisms are studied and the methods used to study them: biochemistry examines the fundamental chemistry of life; molecular biology studies the complex interactions of systems of biological molecules; cellular biology examines the basic building block of all life, the cell; physiology examines the physical and chemical functions of the tissues and organ systems of an organism; and ecology examines how various organisms and their environment interrelate.

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一、設Xi～N( 3，0.16)，求以下各題之機率值或Y值：

1. 由此常態母體中抽出 n = 4 的隨機樣品：

X-bar～N( 3，0.16/4)，其中 X-bar = ΣXi，i = 1, 2, 3, 4.

(a) P( X-bar < 2.5 )

2.5 - 3

= P( Z < -----------------)

√( 0.16/4)

= P( Z < -2.5 )

= 0.0062

(b) P( X-bar > Y )

Y - 3

= P( Z > --------------- )

√( 0.16/4)

= P( Z > 1.8808 )

= 0.03

∴ Y = 3 √( 0.16/4) 1.8808 = 3.3762

2. 由此常態母體中抽出 n = 15 的隨機樣品：

X-bar～N( 3，0.16/15)，其中 X-bar = ΣXi，i = 1, 2, …, 15.

(c) P( 2.8 < X-bar <3.8 )

= P( X-bar < 3.8 ) - P( X-bar < 2.8 )

3.8 - 3 2.8 - 3

= P( Z < ----------------- ) - P( Z < ------------------ )

√( 0.16/15) √( 0.16/15)

= P( Z < 7.7460 ) - P( Z < -1.9365 )

= 1.0000 – 0.0246

= 0.9736

(d) P( Y< X-bar <3 )

= P( X-bar < 3 ) - P( X-bar < Y )

3 – 3 Y - 3

= P( Z < ------------------- ) - P( Z < ------------------- )

√( 0.16/15) √( 0.16/15)

= P( Z < 0 ) - P( Z < -0.4399 )

= 0.5 – 0.33

= 0.17

∴ Y = 3 √( 0.16/15) -0.4399 = 2.9546

二、某大學學校學生心理測驗分數呈常態分布，平均為500，標準差為50，試問：

1. 某位學生的分數是高於510的機率為何？低於400？

X1～N( 500，502)

(a) P( X1 > 510 )

510 - 500

= P( Z > ----------------- )

50

= P( Z > 0.2 )

= 0.4207

(b) P( X1 < 400 )

400 - 500

= P( Z < ----------------- )

50

= P( Z < -2 )

= 0.0228

2. 若隨機抽出16位學生，求他們的平均分數介於480到520的機率為何？

X-bar～N( 500，502/16)，其中 X-bar = ΣXi，i = 1, 2, …, 16.

P( 480 < X-bar < 520 )

= P( X-bar < 520 ) – P( X-bar < 480 )

520-500 480-500

= P( Z < ---------------- ) - P( Z < ----------------- )

√( 502/16) √( 502/16)

= P( Z < 1.6 ) - P( Z < -1.6 )

= 0.9452 – 0.0548

= 0.8904

Source(s): 我的求學過程…