Question

Suppose that the distribution Of typing speed in words per minute for experience typists using a new type of split keyboard can be approximated by a normal curve with a mean 64 words per minute and standard deviation 16 words per minute.

a) what is the probability that a randomly selected typist speed is At most 64 wpm?

b) What is the probability that a randomly selected typing speed is less than 64 words per minute?

c) what is the probability that a randomly selected typist speed is between 48 and 96 words per minute? (round your answer to four decimal places.)

Answer 1

Solution :

Given

Mean=64

Standard deviation =16

Use the z scores table z=(x-bar-mu) /s

a)

P(X<=64) =P(Z<=(64-64)/16)

= P(Z<= 0)

= 0.5

The requried probability is 0.5

b)

P(X<64) =P(Z<(64-64)/16)

=P(Z<0)

= 0.5

The requried probability is 0.5

c)

P( 48<X<96) = P((48-64)/16<Z<(64-64)/16)

=P( - 1<Z<0)

=P(Z< 0) - P(Z<-1)

= 0.5 - 0.1586553 = 0.3413447

= 0.3413

The requried probability is 0.3413

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