Kindly send all answers:

1. Given a standard normal distribution, find the area under the curve that lies:

• a. to the right of z = 0.24;
• b. to the right of z = 2.21
• c. to the left of z = 3.15;
• d. between z = 0.80 and z = 1.46
• e. to the left of z = 1.20;
• f. between z = 1.10 and z = 0.15;

2. Given a normal distribution with = 40 and = 8, find

• a. the value of x that has 70% of the normal curve area to the left;
• b. the normal curve area to the left of x = 12;
• c. the normal curve area between x = 22 and x = 38;
• d. the normal curve area to the right of x = 15;
• e. the two values of x that contain the middle 70% of the normal curve area

3. The sick leave time of employees in a firm in a month is normally with a mean of 100 hours and a standard deviation of 20 hours.

• a. Find the probability that the sick - leave time of an employee in a month exceeds 140 hours.

4. The heights of 1000 students are normally distributed with a mean of 184.5 centimeters and a standard deviation of 10.5 centimeters. Assuming that the heights are recorded to the nearest half-centimeter, how many of these students would you expect to have heights.

• a. equal to 125.0 centimeters?
• b. less than 150.0 centimeters?
• c. between 161.5 and 192.0 centimeters inclusive?
• d. greater than or equal to 178.0 centimeters?

NOTE: FOUR DECIMALS NEEDED, HANDWRITTEN SOLUTIONS. THANK YOU