Average 10.Variance 25.00. sample of 30 students. Find the probability that I). less than 8.00 ? II).between 8.00 and 13.00 ?

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Feb 7, 2018

Answer:

#"I) P = 0.3085"#
#"II) P = 0.4495"#

Explanation:

#"variance = 25" => "standard deviation "= sqrt(25)=5#
#"We go from N(10, 5) to normalized normal distribution :"#
I)
#z =(7.5 - 10)/5 = -0.5#
#=> P = 0.3085 " (table for z-values)"#
II)
#z = (13.5 - 10)/5 = 0.7#
#=> P = 0.7580 " (table for z-values)"#
#=> P("between 8 and 13") = 0.7580 - 0.3085 = 0.4495#

#"7.5 and 13.5 instead of 8 and 13 because of a continuity"#
#"correction to the discrete values."#

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