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Fiesta28 [93]
3 years ago
6

Add an intersection the red light times normally distributed by the mean of three minutes and a standard deviation of .25 minute

s approximately what percent of red lights last between 2.5 and 3.5 minutes
Mathematics
1 answer:
Soloha48 [4]3 years ago
8 0

95% of red lights last between 2.5 and 3.5 minutes.

<u>Step-by-step explanation:</u>

In this case,

  • The mean M is 3 and
  • The standard deviation SD is given as 0.25

Assume the bell shaped graph of normal distribution,

The center of the graph is mean which is 3 minutes.

We move one space to the right side of mean ⇒ M + SD

⇒ 3+0.25 = 3.25 minutes.

Again we move one more space to the right of mean ⇒ M + 2SD

⇒ 3 + (0.25×2) = 3.5 minutes.

Similarly,

Move one space to the left side of mean ⇒ M - SD

⇒ 3-0.25 = 2.75 minutes.

Again we move one more space to the left of mean ⇒ M - 2SD

⇒ 3 - (0.25×2) =2.5 minutes.

The questions asks to approximately what percent of red lights last between 2.5 and 3.5 minutes.

Notice 2.5 and 3.5 fall within 2 standard deviations, and that 95% of the data is within 2 standard deviations. (Refer to bell-shaped graph)

Therefore, the percent of  red lights that last between 2.5 and 3.5 minutes is 95%

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