Question

A safety light is designed so that the times between flashes are normally distributed with a mean of 5.00 s and a standard deviation of 0.70 s

a. Find the probability that an individual time is greater than 6.00 s

.b. Find the probability that the mean for 50 randomly selected times is greater than 6.00

c. Given that the light is intended to help people see an​ obstruction, which result is more relevant for assessing the safety of the​ light?

a. The probability is approximately .

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Answer 1

GIVEN:

Let X represents the times between flashes of safety light which are normally distributed with a mean of and a standard deviation of .

(a) PROBABILITY THAT AN INDIVIDUAL TIME IS GREATER THAN 6.00s:

To calculate the probability, we convert the raw score X into standard score Z using the formula given by,

The probability that an individual time greater than 6.00 is given by,

  

  

   {Since }

Using the z table, the probability value is the value with corresponding row 1.4 ad column 0.03.

The probability that an individual time greater than 6.00 is .

(b) PROBABILITY THAT MEAN OF 50 RENDOMLY SELECTED TIMES IS GREATER THAN 6.00s:

To calculate the probability, we convert the mean score into standard score Z using the formula given by,

The probability that mean of 50 selected time greater than 6.00 is given by,

  

  

   {Since }

Using the z table, the probability value is the value with corresponding row 10.1 and column 0.00.

The probability that mean of 50 selected time greater than 6.00 is 0.

(c) RESULT THAT IS MORE RELEVANT FOR ASSESSING THE SAFETY OF LIGHT:

The first result is more relevant. We should check that every single light works properly, not all of the lights on average.