Question

2.1 The annual salaries of employees in a large company are approximately normally distributed with a mean of R50 000 and a standard deviation of R 20 000.

Calculate the percentage of employees who earn:

2.1.1 less than R40
000?

2.1.2 between R45 000 and R65
000?
2.1.3 more than R70,000?

2.2 The long-distance calls made by the employees of a company are normally distributed with a mean of 6.3 minutes and a standard deviation of 2.2 minutes.

Find the probability that a call:

2.2.1 Lasts between 5 and 10 minutes.

2.2.2 Lasts more than 7 minutes.

2.2.3 Lasts less than 4 minutes

2.3** ** The
probability that a driver must stop at any one traffic light coming
Regent Business
school beach
Campus is 0.2. There are 15 sets of traffic lights on the
journey.

What is the probability that a student:

2.3.1 must stop at exactly 2 of the 15 sets of traffic lights?

2.3.2 will be stopped at 1 or more of the 15 sets of traffic lights?

2.4 The number of typing mistakes made by a secretary has a Poisson distribution. The mistakes are made independently at an average rate of 1.65 per page. Find the probability that a three-page letter contains no mistakes.

Answer #1

P(X < A) = P(Z < (A - mean)/standard error)

2.1) Mean = 50,000

Standard deviation = 20,000

2.1.1) P(X < 40,000) = P(Z < (40,000 - 50,000)/20,000)

= P(Z < - 0.5)

= 0.3085

2.1.2) P(45,000 < X < 65,000) = P(X < 65,000) - P(Z < 45,000)

= P(Z < (65,000 - 50,000)/20,000) - P(Z < (45,000 - 50,000)/20,000)

= P(Z < 0.75) - P(Z < - 0.25)

= 0.7734 - 0.4013

= 0.3721

2.13) P(X > 70,000) = 1 - P(X < 70,000)

= 1 - P(Z < (70,000 - 50,000)/20,000)

= 1 - P(Z < 1)

= 1 - 0.8413

= 0.1587

2.2.1) P(5 < X < 10) = P(X < 10) - P(X < 5)

= P(Z < (10 - 6.3)/2.2) - P(Z < (5 - 6.3)/2.2)

= P(Z < 1.68) - P(Z < - 0.59)

= 0.9535 - 0.2776

= 0.6759

2.2.2) P(X > 7) = 1 - P(X < 7)

= 1 - P(Z < (7 - 6.3)/2.2)

= 1 - P(Z < 0.32)

= 1 - 0.6255

= 0.3745

2.2.3) P(X < 4) = P(Z < (4 - 6.3)/2.2)

= P(Z < 1.05)

= 0.8531

The annual salaries of employees in a large company are
approximately normally distributed with a mean of $50,000 and a
standard deviation of $2000. In a sample of 20 employees, what is
the probability their mean salary is greater than or equal to
$60,000? (3 decimal places)

2.1 A stock price has an expected return of 15% and a volatility
of 25%. It is currently $56.
2.1.1 What is the probability that it will be greater than $85 in
two years? (4)
2
2.1.2 What is the stock price that has a 5% probability of being
exceeded in two years? (2)
2.2 A binary option pays off $150 if a stock price is greater than
$40 in three months. The
current stock price is $35 and its...

a. The annual salaries of employees in a large company are
approximately normally distributed with a mean of $50,000 and a
standard deviation of $2000. What proportion of employees earned
between $45,000 to $55,000? (3 decimal places)
b. The annual salaries of employees in a large company are
approximately normally distributed with a mean of $50,000 and a
standard deviation of $2000. What is the probability of randomly
selecting one employee who earned between $45,000 to $55,000? (3
decimal places)

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