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The annual commissions per salesperson employed by a manufacturer of light machinery averaged $40,000 with a standard deviation of $5,000. What percent of the sales persons earn between $32,000 and $42,000?
A) 60.06%.
B) 39.94%.
C) 34.13%.
D) 81.66%.

Respuesta :

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Answer:

A

Explanation:

From the given information;

The required probability needed to carry out is P(32000<X<42000);

Given that:

mean [tex]\mu[/tex] = 40000

standard deviation [tex]\sigma[/tex] = 5000

Using the standard normal distribution;

[tex]P(32000 <X<42000) = ( \dfrac{x - \mu}{\sigma} <Z< \dfrac{x - \mu}{\sigma})[/tex]

[tex]P(32000 <X<42000) = ( \dfrac{32000 - 40000}{5000} <Z< \dfrac{42000 - 40000}{5000})[/tex]

[tex]P(32000 <X<42000) = ( -1.6<Z<0.4)[/tex]

Here, the region of the area lies between -1.60 and 0.40

∴

P(320000 < X < 40000) = P(Z<0.40) - P(Z< -0.40)

From Z tables;

P(320000 < X < 40000) =  0.6554 -0.0548

P(320000 < X < 40000) = 0.6006

P(320000 < X < 40000) = 60.06%

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