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jek_recluse [69]
3 years ago
11

Henry has collected data to find that the typing speeds for the students in a typing class has a normal distribution. What is th

e probability that a randomly selected student has a typing speed of less than 51 words per minute if the mean is 47 words per minute and the standard deviation is 4 words per minute
Mathematics
1 answer:
Mekhanik [1.2K]3 years ago
8 0

Answer: 0.8413

Step-by-step explanation:

Given : Henry has collected data to find that the typing speeds for the students in a typing class has a normal distribution.

Mean : \mu=47

Standard deviation : \sigma= 4

Let x be the random variable that represents the typing speeds for the students.

The z-score :-

z=\dfrac{x-\mu}{\sigma}

For x= 51

z=\dfrac{51-47}{4}=1

Using the standard normal distribution table ,the probability that a randomly selected student has a typing speed of less than 51 words per minute :-

P(x

Hence, the probability that a randomly selected student has a typing speed of less than 51 words per minute = 0.8413

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Elden [556K]

Hello from MrBillDoesMath

Answer:

[email protected] = - sqrt(7)/ 4    

which is choice B

Discussion:

This problem can be solved by drawing triangles and looking at ratios of sides or by using the trig identity:

([email protected])^2 + (sin2)^2 = 1

If [email protected] = 3/4 , the

([email protected])^2 + (3/4)^2 = 1 =>              (subtract (3/4)^2 from both sides)

([email protected])^2 = 1 - (3/4)^2  = 1 - 9/16   = 7/16

So...... taking the square root of both sides gives

[email protected] =  +\- sqrt(7)/ sqrt(16) = +\- sqrt(7)/4

But is [email protected] positive or negative?  We are told that @ is in the second quadrant and cos(@) is negative in this quadrant, so our answer must be negative

[email protected] = - sqrt(7)/ 4    

which is choice B


Thank you,

Mr. B


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