Question

Suppose it is known that the weights of a certain group of individuals are approximately normally distributed with a mean of 140 pounds and a standard deviation of 25 pounds. What is the probability that a person picked at random from this group will weigh between 100 and 170 pounds?

Answer #1

Given = 140 , = 25

We convert this to standard normal as

P(X < x) = P( Z < ( X - ) / )

P ( 100 < X < 170 ) = P(X < 170) - P(X < 100)

= P ( Z < ( 170 - 140 ) / 25 ) - P ( Z < ( 100 - 140 ) / 25 )

= P ( Z < 1.2) - P ( Z < -1.6 )

= 0.8849 - 0.0548 (From Z table)

= **0.8301 **

Suppose that the weights of professional baseball players are
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Suppose that the weights of professional baseball players are
approximately normally distributed, with a mean of 207 pounds and
standard deviation of 24 pounds.
What proportion of players weigh between 200 and 250
pounds?
What is the probability that the mean weight of a team of 25
players will be more than 215 pounds?
Could you please explain too?

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