The citizens of Villopolis have normally distributed body weights with a mean of

Question

The citizens of Villopolis have normally distributed body weights with a mean of 197 lbs. and a standard deviation of 20 lbs. What is the probability that a randomly chosen citizen will have a body weight lower than 221 lbs? Round your answer to 3 decimal places.

Widgets manufactured by the Townburg Widget Company have normally distributed lifespans with a mean of 113 months and a standard deviation of 14 months. What is the probability that a randomly chosen widget will still be usable after 121 months? Round your answer to 3 decimal places.

The Polisburg Parks Department has just installed 1500 new lightbulbs with an expected mean lifespan of 75 months and a lifespan standard deviation of 13 months. Assuming normally distributed bulb failure, how many bulbs will need to be replaced after 53 months? Round your asnwer to the nearest whole number.

The University of Poliston gives a full scholarship to any student who scores in the top 6% of students on the SMRT standardized exam. SMRT scores have a mean of 280 and a standard deviation of 38. What score does a student need to attain in order to receive the scholarship? Round your answer to the nearest whole number?

Explanation / Answer

1) probability that a randomly chosen citizen will have a body weight lower than 221 lbs=P(X<221)

=P(Z<(221-197)/20)=P(Z<1.2)=0.885

2)probability that a randomly chosen widget will still be usable after 121 months=P(X>121)

=1-P(X<121)=1-P(Z<(121-113)/14) =1-P(Z<0.5714)=1-0.716 =0.284

3)

probability that bulb fail with in 53 months =P(X<53) =P(Z<(53-75)/13)=P(Z<-1.6923)=0.045

therefore bulbs needs to be replaced after 53 months =np=1500*0.045=67.5~ 68

4)for top 6 percentile ; z=1.5548

therefore corresponding score =mean +z*std deviation =280+1.5548*38= ~339

please revert for any clarification required,.

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