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malfutka [58]
3 years ago
11

The time that it takes a randomly selected job applicant to perform a certain task has a distribution that can be approximated b

y a normal distribution with a mean value of 150 sec and a standard deviation of 15 sec. The fastest 10% are to be given advanced training. What task times qualify individuals for such training? (Round the answer to one decimal place.)
Mathematics
1 answer:
zepelin [54]3 years ago
8 0

Answer:

If the task is performed in less than or equal to 130.8 seconds, then, the individuals qualify for advanced training.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 150 sec

Standard Deviation, σ = 15 sec

We are given that the distribution of time taken is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

We have to find the value of x such that the probability is 0.10

P(X < x)  

P( X < x) = P( z < \displaystyle\frac{x - 150}{15})=0.10  

Calculation the value from standard normal z table, we have,  

\displaystyle\frac{x - 150}{15} = -1.282\\x = 130.8  

Thus, if the task is performed in less than or equal to 130.8 seconds, then, the individuals qualify for advanced training.

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3 years ago
: A sports store sells a total of 70 soccer balls in one month, and collects a total of $2,400. A limited Edition soccer ball is
sweet-ann [11.9K]

Answer:

The store sold 43 pro NSL soccer balls.

The store sold 27 limited Edition soccer balls.

Step-by-step explanation:

Let x represent number of limited Edition soccer balls and y represent the number of pro NSL soccer balls.

We have been given that a sports store sells a total of 70 soccer balls in one month. We can represent this information in an equation as:

x+y=70...(1)

Cost of x limited Edition soccer balls: 65x

Cost of y pro NSL soccer balls: 15x

We are also told that store collected a total of $2,400. We can represent this information in an equation as:

65x+15y=2400...(2)

From equation (1), we will get:

x=70-y

Substituting this value in equation (2), we will get:

65(70-y)+15y=2400

4550-65y+15y=2400

4550-50y=2400

4550-4550-50y=2400-4550

-50y=-2150

\frac{-50y}{-50}=\frac{-2150}{-50}

y=43

Therefore, the store sold 43 pro NSL soccer balls.

Now, we will substitute y=43 in equation (1) to solve for x:

x+43=70

x+43-43=70-43

[tex]x=27/tex]

Therefore, the store sold 27 limited Edition soccer balls.

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3 years ago
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