a Ques son Hobo The reading speed of second grade students is approximately norm

Question

a Ques son Hobo The reading speed of second grade students is approximately normal with a mean of 89 words per mmute (wpm)and a standard dewation of 10 wpm Complete parts (a) though (a) What is the probability a randomly selected student will read more than 94 words per minute? The probability is Round to four decimal paces as needed (b) what is the probabiit that a random sample of 12 second grade stuse resuis in amean read ng fato ormore than 94 words per minute? The probabity (Round to four decimal pocos as needed) (c) What the probobility that random soniple of 24 second grade students results in a mean readng rate of more than g4 words per mmute? The probability is (Round to four decimal places as needed)

Explanation / Answer

a)P(X>94)=1-P(Z<(94-89)/10)=1-P(Z<0.5)=1-0.6915=0.3085

b)std error of mean =std deviation/(n)1/2 =2.8868

hence P(X>94)=1-P(Z<(94-89)/2.8868)=1-P(Z<1.7321)=1-0.9584=0.0416

c)

std error of mean =std deviation/(n)1/2 =2.0412

hence P(X>94)=1-P(Z<(94-89)/2.8868)=1-P(Z<2.4495)=1-0.9928=0.0072

d) option A is correct

e)std error =std deviation/(n)1/2 =2.236

hence P(X>91.6)=1-P(Z<(91.6-89)/2.236)=1-P(Z<1.1628)=1-0.8775=0.1225

option B ; or more is 0.1225

f) for top 5 %, z=1.96

hence coresponding value =89+1.96*2.236 =93.4

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