Normal Distribution

Which of the following are properties of Normal Distribution? Choose all that apply.

• symmetric

• bell-shaped

• positively skewed

• negatively skewed

• mound-shaped

Total area under the curve of Normal Distribution is equal to ______ .

Suppose an average adult drinks 3 liters of water per day. Let's suppose water consumption is normally distributed with a standard deviation of 0.4 liters. What is the z score for someone who drinks 4 liters per day? Round your answer to the nearest one decimal value.

The distribution of the annual incomes of a group of employees at Compton Plastics approximates a normal distribution with a mean of $30,000 and a standard deviation of $2000. About 95% of the incomes lie between what two amounts?

• $27,000 and $33,000

• $28,000 and $36,000

• $26,000 and $34,000

• $30,000 and $34,000

The marks obtained by the students are normally distributed with mean 61 marks and variance 100 marks. Find the probability that randomly chosen student obtains at least 85 marks.

• 0.0082

• 0.4207

• 0.1112

• 0.9918

• 0.1424

Suppose the length of time to find a parking space at 10:00 am around the university campus follows a normal distribution with a mean of five minutes and a standard deviation of two minutes.

Find the probability that it takes exactly 5 minutes to find a parking spot.

• 0.5404

• 0.4806

• 0.5747

• 0.6802

• 0.3418

Suppose the Internal Revenue Service (IRS) reported that the mean tax refund for the year 2020 was $2,800. Assume the standard deviation is $450 and the amounts refunded follow a normal distribution.

What percent of the refunds are more than $2,500?

Round your final answer to the nearest integer value.

Suppose the Internal Revenue Service (IRS) reported that the mean tax refund for the year 2020 was $2,800. Assume the standard deviation is $450 and the amounts refunded follow a normal distribution.

How much money did the 95th percentile receive in 2020?

• $3,600

• $2,790

• $4,250

• $3,540

• $3,420

A woman lives on the 40th floor of Nest One building in Tashkent. When it is raining she takes the elevator to the 40th floor. But when it is sunny, she goes to 35th floor with an elevator and takes the stairs the rest of the way. Why?