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3 years ago

Need help with this please.

Mathematics

1 answer:

iogann1982 [59]3 years ago

4 0

Hi....

Im not sure if i got it right but i think its: 1.8........ Hope this helps. Brainliest Please

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3 years ago

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Complete Question

A population has a mean of 25, a median of 24, and a mode of 26. The standard deviation is 5. The value of the 16th percentile is _______. The range for the middle 3 standard deviation is _______.

Answer:

The value of the 16th percentile is $x = 20$

The range for the middle 3 standard deviation is $10 \to 40$

Step-by-step explanation:

From the question we are told that

The mean is $\mu = 25$

The median is $m = 24$

The mode is $n = 26$

The standard deviation is $\sigma = 5$

Generally the 16th percentile is mathematically represented as

$P(x)= P(\frac{X - \mu }{ \sigma } \le \frac{x- 25 }{5} ) = 0.16[/teGenerally [tex]\frac{X - \mu}{\sigma } = Z(The \ standardized \ value \ of \ X )$

$P(x) = P(Z \le \frac{ x - 25}{5} ) = 0.16$

Now from the normal distribution table the z-score of 0.16 is

z = -1

$P(x) = P(Z \le \frac{ x - 25}{5} ) = P(Z \le -1 )$

=> $\frac{x- 25}{5} = -1$

=> $x- 25 = -5$

=> $x = 25-5$

=> $x = 20$

The range for the middle 3 standard deviation is mathematically represented

$\mu - 3\sigma \to \mu + 3\sigma$

$25 - 3(5 ) \to 25 + 3(5 )$

$10 \to 40$

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