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A course for a snail race has times that are skewed right with a mean of 5. 18 minutes and a standard deviation of 2. 34 minutes. If a random sample of 38 snails is selected, what is the probability that the mean race time is less than 4. 3 minutes? 0. 0102 0. 3534 0. 6466 0. 9098

Sagot :

onyebuchinnaji

The probability that the mean race time is less than 4. 3 minutes is 0.3534.

Normal distribution curve

A normal distribution curve can be used to determine the probability of selecting a mean race time less than 4.3 minutes.

In normal distribution curve

  • Mean = median = 50%
  • 1 standard deviation below the mean (M - d) = 16%

Time of race at 1 standard deviation below the mean

5.18 - 1(2.34) = 2.84 minutes

4.3 minutes is greater than 2.84 minutes but less than 5.18 minutes.

Apply interpolation method to determine the probability corresponding to 4.3 minutes.

5.18 ---------------- 50%

4.3 ------------------- ?

2.84 ----------------- 16%

[tex]\frac{5.18 - 4.3}{5.18 - 2.84} = \frac{50 - x}{50-16} \\\\0.376 = \frac{50-x}{34} \\\\50-x = 12.78\\\\x = 50 - 12.78\\\\x = 37.2 \ \%[/tex]

x = 0.37

The area of normal distribution curve is not equal at all points, it is more towards the center and less towards the left. The probability will shift little to left, with a value of 36% or 35%.

Thus, the probability that the mean race time is less than 4. 3 minutes is 0.3534.

Learn more about normal distribution curve here: https://brainly.com/question/14644201

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