Question

In: Statistics and Probability

The distribution of ages of all the employees in Company X follows a normal distribution. The...

The distribution of ages of all the employees in Company X follows a normal distribution. The average age is 40 and the standard deviation is 5.

Find the Z-score of a 50 year old employee.

What is the probability that a randomly chosen employee will be younger than 35 years?

What is the probability that a randomly chosen employee will have an age between 35 and 45 years?

What is the probability that a randomly chosen employee will be older than 55 years?

Find the Z-score of a 35 year old employee.

Solutions

Expert Solution

Solution :

Given that ,

mean = = 40

standard deviation = = 5

a.using z score formula

z =(X- ) / = 50 -40 / 5=2

P(X< 35) = P[(X- ) / < (35-40) /5 ]

= P(z < -1)

Using z table

= 0.1587

P(35< x <45 ) = P[(35 - 40) /5 < (x - ) / < (45 - 40) / 5)]

= P(-1< Z <1 )

= P(Z < 1) - P(Z < -1)

Using z table

= 0.8413-0.1587

probability= 0.6826

P(x > 55) = 1 - P(x< 55)

= 1 - P[(x -) / < (55-40) /5 ]

= 1 - P(z <3 )

Using z table

= 1 - 0.9987

= 0.0013

probability= 0.0013

using z score formula

z =(X- ) / = 35 -40 / 5=-1

orchestra answered 11 months ago

Next > < Previous

Related Solutions

Assume the length X of a certain unit follows the normal distribution with a mean of...

Assume the length X of a certain unit follows the normal distribution with a mean of 50mm and a standard deviation of 5 mm. If a random sample of 21 units is taken, find the value C such that Probability(sample variance > C) = 0.90

assuming the length X of a certain unit follows the normal distribution with a mean of...

assuming the length X of a certain unit follows the normal distribution with a mean of 50mm and a standard deviation of 5mm. if a random sample of 21units is taken, find the value C such that probability (sample variance > C)= 0.90

The random variable X follows a normal distribution with a mean of 10 and a standard...

The random variable X follows a normal distribution with a mean of 10 and a standard deviation of 3. 1. What is P(7≤X≤13)? Include 4 decimal places in your answer. 2. What is the value of k such that P(X>k)=0.43? Include 2 decimal places in your answer.

X follows a normal distribution with mu = 4.7 and sigma = 1.1. P(3.05 < X...

X follows a normal distribution with mu = 4.7 and sigma = 1.1. P(3.05 < X < 3.93) to four decimal places is: 1) 0.6752 2) 0.1752 3) 0.3248 4) 0.8248

1) Let x be a continuous random variable that follows a normal distribution with a mean...

1) Let x be a continuous random variable that follows a normal distribution with a mean of 321 and a standard deviation of 41. (a) Find the value of x > 321 so that the area under the normal curve from 321 to x is 0.2224. Round your answer to the nearest integer. The value of x is_______ (b) Find the value of x so that the area under the normal curve to the right of x is 0.3745. Round...

The following are the ages of all employees of a small company: 18, 56, 40, 40,...

The following are the ages of all employees of a small company: 18, 56, 40, 40, 51,51 56, 45, 48, 49 ,70 a) Find the sample mean b) Find the sample median c) Find the sample mode d) Find .the sample range e) Find the lower and upper quartiles, and the sample interquartile range IQR Q1= Q3= IQR= f) Display the data with a boxplot (with fences andwhiskers). Calculate Fences: g) Write a brief description of this data (symmetry, outliers)....

The annual production of a manufacturing company that produces generators follows a normal distribution with a...

The annual production of a manufacturing company that produces generators follows a normal distribution with a mean µ=1200 and standard deviation σ=100. 1) The shading area for the probability between 1100 and 1300 units is? 2) The probability of producing between 1100 and 1350 units is ? 3) The probability of producing less than 1200 units is? 4) The probability of producing between 1200 and 1350 units is . 5) A student intends to measure the boiling temperature of a...

The LDL cholesterol level of all men aged 20 to 34 follows the Normal distribution with...

The LDL cholesterol level of all men aged 20 to 34 follows the Normal distribution with mean μ=120μ=120 milligrams per deciliter and the standard deviation is σ=30σ=30 milligrams per deciliter. If you choose an SRS of 25 men from this population, what is the sampling distribution of mean cholesterol level of the 25 selected men. Select one: a. x¯∼N(120,1.2)x¯∼N(120,1.2) b. Couldn't decide c. x¯∼N(120,30)x¯∼N(120,30) d. x¯∼N(120,6)

1. Suppose X follows the normal distribution with mean μ and variance σ^2 . Then: (Circle...

1. Suppose X follows the normal distribution with mean μ and variance σ^2 . Then: (Circle all that apply.) A. X is symmetric with respect to the y-axis. B. P(X=2)=P(X=-2). C. Y=aX follows the same distribution as X, where a is a constant. D. None of the above statements is correct. 2. Given a random variable X having a normal distribution with μ=50, and σ=10. The probability that Z assumes a value between 45 and 62 is: ___________. 3. Which...

Let X be a random variable which follows normal distribution with mean 12 and variance 0.25....

Let X be a random variable which follows normal distribution with mean 12 and variance 0.25. Then find the following probabilities (a) P( X ≤ 15 ) (b) P( X ≤ 17.5 ) (c) P( |X-15| ≤ 3 )

Subjects