The reading speed of second grade students in a large city is approximately normal, with a mean of 90 words per minute (wpm) and a standard deviation of 10 wpm. complete parts (a) through (f). (a) what is the probability a randomly selected student in the city will read more than 96 words per minute?
Accepted Solution
A:
Answer: 0.2743Step-by-step explanation:Given : The reading speed of second grade students in a large city is approximately normal, with a mean of [tex]\mu=90[/tex] words per minute (wpm) and a standard deviation of [tex]\sigma=10[/tex] wpm. Let x be the random variable that represents the reading speed of second grade students.z-score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]For x= 96 words per minute [tex]z=\dfrac{96-90}{10}=0.6[/tex]Now, the probability a randomly selected student in the city will read more than 96 words per minute will be :-[tex]P(x>96)=P(z>0.6)=1-P(\leq0.6)\\\\=1- 0.7257469=0.2742531\approx0.2743[/tex]Hence, the probability a randomly selected student in the city will read more than 96 words per minute = 0.2743