Question

7. The time taken to assemble a car in a certain plant is a normal random variable having a mean of 20 hours. If 6.3% of the cars assembled take longer than 25 hours to assemble, what is the standard deviation of assembly time?

Answer 1

Answer:

ANSWER

TIme taken to assemble follows normal distribution.

Given mean i.e. μ =20 hours

Given standard deviation i.e. σ =2 hours

The normal random variable of a standard normal distribution is called a standard score or a z-score. Every normal random variable X can be transformed into a z score via the following equation:

z=(X−μ)/σ

where X is a normal random variable, μ is the mean of X, and σ is the standard deviation of X.

For X=22

Z=(22−20)/2=1

For X=20

Z=(20−20)/2=0

P(a<X<b)=P(X<b)–P(X<a) as understood from diagram

P(20<X<22)=P(X<22)−P(X<20)

=P(Z<1)−P(Z<0)

=0.3413

Step-by-step explanation:

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