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Artist 52 [7]
2 years ago
10

A normal population has a mean of 20.0 and a standard deviation of 4.0.

Mathematics
1 answer:
Tanya [424]2 years ago
3 0
<h2><em>a) </em><u>The z-value associated with 25.0</u></h2><h2>Z = 1.25</h2><h2 /><h2><em>b)</em> <u>proportion of the population is between 20.0 and 25.0 is</u></h2><h2>Proportion = 0.3944</h2><h2 /><h2><em>c)</em> <u>proportion of the population is less than 18.0 is</u></h2><h2>Proportion = 0.3085</h2>

Calculations:

Normal pop has mean of 20.0

standard deviation = 4.0

XNN(20.0, 4.0)

a).

z=\frac{x-h}{z}

=\frac{25-20}{4.0} =\frac{5}{4} =1.25

<u>Z = 1.25</u>

<u></u>

b).

The proportion between 20 and 25 is P(20 <x<25.0)

=p(\frac{20-20}{4} < z < \frac{25-0}{4} )

=P(0 < z < 1.25)

=P(Z < 1.25)-P(z < 0)

=0.8944-0.5000

P(20 < x < 25)=0.3944

c).

The proportion value is less than 18 when

P(x < 18)=p(\frac{x--4}{6} < \frac{18-20}{4}

=P(z < \frac{-2}{4})

=P(z < -0.5)

P(x<18) = 0.3085

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