Use the following information for the next three (3) questions The reading speed

Question

Use the following information for the next three (3) questions The reading speed of sixth-grade students is normally distributed, with a mean speed of 125 words per minute and a standard deviation of 24 words per minute 27. Find the probability that a randomly selected student will have a reading speed be- tween 114 and 132 words per minute. (a) 0.2913 (b) 0.4247 (c) 0.6772 (d) 0.3228 28. If twelve sixth graders are randomly selected, what is the probability that their mean reading speed is greater than 140 words per minute? (a) 0.2643 (b) 0.7357 (c) 0.9850 (d) 0.015 29. what is the minimum reading speed needed to be in the top 10% of sixth-graders? (a) 147 (b) 134 (c) 156 (d) 125

Explanation / Answer

Solution:- Given that mean = 125 , sd = 24   

Formula Z = (x - )/

27) P(114 < X < 132) = P((114-125)/24 < Z < (132-125)/24)
= P (0.4583 < Z < 0.2917)
= 0.2913

=> option a) 0.2913

28) P(X < 140) = P(Z > (140-125)/24)
= P (Z > 0.625)
= 1 P(Z < 0.625)
= 1 0.7357
= 0.2643
  
=> option a) 0.2643

29) P((X - 125)/24 = 0.10
(X - 125)/24 = 1.28
X = 125 + (24*1.28)
X = 155.72
X = 156

=> option C) 156
  

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