The average age of UST employees is 34 years old. Assume the data is n

Nicontio1

Nicontio1

Answered question

2021-12-09

The average age of UST employees is 34 years old. Assume the data is normally distributed. If the standard deviation is 3 years, find the probability that the age of a randomly selected UST employees will be in the range between 25 and 40 years old.The average age of UST employees is 34 years old. Assume the data is normally distributed. If the standard deviation is 3 years, find the probability that the age of a randomly selected UST employees will be in the range between 25 and 40 years old.

Answer & Explanation

Neunassauk8

Neunassauk8

Beginner2021-12-10Added 30 answers

Step 1
Let W be a random variable representing the age of the employees.
The average age of the UST employees is μ=34 years old.
The standard deviation is σ=3 years.
In the given scenario, the random variable W is normally distributed.
It can be mathematically represented as:
WN(μ,σ2)
N(34,32)
Step 2
The probability that the age of a randomly selected UST employees will be in the range between 25 and 40 years is calculated as:
P(25<W<40)=P(25343<Wμσ<40343)
=P(3<Z<2)
=P(Z<2)P(Z<3)
=P(Z<2)(1P(Z<3))
=0.9772(10.9987) (from Z table)
Thus, the probability that the age of a randomly selected UST employees will be in the range between 25 and 40 years is 0.9759.

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