问题 解答题
经销某品牌的汽车,顾客通常采用分期付款的方式购车.根据以往资料统计,付款期数X的分布列为:
X12345
P0.40.20.20.10.1
经销该品牌的汽车,若采用1期付款,其利润为104元;分2期或3期付款,其利润为1.5×104元;分4期或5期付款,其利润为2×104元.
(Ⅰ)求购买该品牌汽车的3位顾客中,至少有1位采用1期付款的概率;
(Ⅱ)记Y为经销一辆该品牌汽车的利润,求Y的分布列及期望E(Y).
答案

(Ⅰ)记“购买该品牌汽车的3位顾客中,至少有1位采用1期付款”为事件A.

.
A
表示事件“购买该商品的3位顾客中无人采用1期付款”.…(2分)

故 P(

.
A
)=(1-0.4)3=0.216,…(4分)

所以P(A)=1-P(

.
A
)=0.784.                                      …(6分)

(Ⅱ)Y的可能取值为104元,1.5×104元,2×104元.                 …(7分)

P(Y=104)=P(X=1)=0.4,

P(Y=1.5×104)=P(X=2)+P(X=3)=0.2+0.2=0.4,

P(Y=2×104)=P(X=4)+P(X=5)=0.1+0.1=0.2.              …(10分)

Y的分布列为:

Y1041.5×1042×104
PF10.40.2
…(11分)

∴E(Y)=104×0.4+1.5×104×0.4+2×104×0.2=1.4×104(元).       …(13分)

阅读理解

Learning to play a musical instrument can change your brain, with a US review finding musical training can lead to improved speech and foreign language skills.

Although it was suggested in the past that listening to Mozart’s music or other classical music could make you smarter, there has been little evidence to show that music can boost(使增长) brain power.

But a data-driven review by Northwestern University has pulled reaserch together that links musical training to learning that spills over into (波及) skills including language, speech, memory, attention and even vocal emotion.

Researcher Nina Kraus said the data strongly suggested that the nervous connections made during musical training also prepared the brain for other aspects of human communication.

“ The effect of musical training suggests that, like physical exercise and its effect on body fitness, music is a resource that tones the brain for auditory fitness and thus requires society to re-examine the role of music in shaping individual development, ” the researchers said in their study.

Kraus said learning musical sounds could improve the brain’s ability to adapt and change and also enable the nervous system to provide constructing patterns that are important to learning.

The study, published in Nature Review Neuroscience , looked at the explosion of research in recent years focusing on the effect of musical training on the nervous system which could have impacts for education.

The study found that playing an instrument prepares the brain to choose what is related in a complex process that may involve reading or remembering a score, timing issues and coordination with other musicians.

小题1:What is the text mainly about ?

A.The effect of physical exercise.

B.The researcher named Kraus.

C.The benefit of musical training.

D.Musicians’ improved skills.小题2:The underlined word “ auditory ” in Paragraph 5 probably means “ __________”.

A.of the body

B.connected with seeing

C.of the mind

D.connected with hearing小题3:It was believed but not proved that listening to classical music could __________.

A.add to your intelligence

B.improve your speech

C.boost your memory

D.make you think faster小题4:According to Kraus, musical training contributes to the following EXCEPT __________.

A.body fitness

B.the way to speak

C.langugage learning

D.mental concentration

多项选择题