Students who have completed a speed reading course have reading speeds that are normally distributed with a mean of 950 words per minute and a standard deviation equal to 220 words per minute. Based on this information, what is the probability of a student reading at more than 1400 words per minute after finishing the course? A) 0.5207 B) 0.4798 C) 0.9798 D) 0.0202

Question

Sierra Hernandez

Mathematics

15 February, 00:45

Students who have completed a speed reading course have reading speeds that are normally distributed with a mean of 950 words per minute and a standard deviation equal to 220 words per minute. Based on this information, what is the probability of a student reading at more than 1400 words per minute after finishing the course? A) 0.5207 B) 0.4798 C) 0.9798 D) 0.0202

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Anton Wilkerson · Answer 1

(D) 0.0202

Step-by-step explanation:

Mean (μ) = 950

Standard deviation (σ) = 220

Pr (x>1400) = ?

Using normal distribution,

Z = (X - μ) / σ

Z = (1400 - 950) / 220

Z = 450/220

Z = 2.05

From the normal distribution table 2.05 = 0.4798

Φ (z) = 0.4798

Don't forget that if Z is positive, Pr (x>a) = 0.5 - Φ (x)

Pr (x>1400) = 0.5 - 0.4798

= 0.0202