Question

The lifetime of an electric guitar is known to follow a normal distribution with mean of 2500 hours and a standard deviation of 300 hours. Find the probability that a randomly selected guitar will last

a.) more than 2000 hours
b.) less than 2600 hours
c.) between 2100 hours and 3200 hours

Answer 1

The probabilities .9525,0.62,0.89.

Given:
Standard deviation = 300hrs
Mean = 2500 hrs
To find: Probability in various conditions.
Solution:
Probability is a branch of arithmetic that handles the incident of a haphazard event. The worth is meant from nothing to individual. Probability has been popularized in Maths to foresee by virtue of what likely occurrences are to take place. The aim of anticipation is fundamentally the extent at which point entity is inclined occur.

This is the basic theory of games, that is still secondhand in the probability distribution, place you will determine the feasibility of consequences for a random experiment. To find the possibility of a distinct occurrence to happen, first, we should see the total number of likely consequences.

Let x = lifetime of an electric guitar
X~N (2500,300)

A. P(p(X>2000)
= 1-P(X<2000)
= 1-2-1.67

= 0.9525
B. p(X>2600)
= 1-P(X<2600)
= 1- 0.327

= 0.6293
C. Z(2.33) - 2 - Z(1.33)

=0.8983

So these are the probabilities  0.9525,0.62,0.89.

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