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  • The mean and standard deviation of a set of 100 observations are 50 and 5 respectively. What is the probability that a randomly selected observation from the set will be greater than 60 ?<div c

The mean and standard deviation of a set of 100 observations are 50 and 5 respectively. What is the probability that a randomly selected observation from the set will be greater than 60 ?

Option: 1

 0.022


Option: 2

0.042


Option: 3

0.012


Option: 4

0.382


Answers (1)

best_answer

The probability that a randomly selected observation from the set will be greater than 60 is:
\mathrm{1 - \mathrm{P} (observation <=60 )}
We can ise the z-score to calculate the probability that an observation is less than or equal to 60 , the \mathrm{ z}-score for an observation of 60 is:
\mathrm{ z=\mid(60-50) / 5=2 }
The probability that an observation is less than or equal to 60 is equal to the probability that a \mathrm{ z }-score is less than or equal to 2 . This probability can be found using the standard normal distribution table which is given as:

\mathrm{ P( observation<=60)=0.9772 }

Therefore, the probability that a randomly selected observation from the set will be greater than 60 is:
\mathrm{ 1-0.9772=0.0228 \text { or } \sim 2.3 \% }

Posted by

Sanket Gandhi

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