# Short answers to the questions

**Question description**

The weight of a bag of corn chips is normally distributed with a mean of 22.2 ounces and a standard deviation of 1.2 ounces.

# 1)

What is the probability that the bag of chips is less than 20 ounces?

# 2)

What is the probability that the bag of corn chips weighs more than 21 ounces?

# 3)

What is the probability that a bag of corn chips weighs between 20.7 and 23.23 ounces?

# 4)

What is the area under the normal curve between z = -1.8 and z = -2.16?

## The next 3 questions refer to the following scenario:

Housing has become more affordable over the past couple of decades, thanks to low inflation and low interest rates. Suppose the distribution of the time that it takes to buy a home can be approximated normally with a mean of 9.5 months and a standard deviation of 2.4 months.

# 5)

What proportion of buyers selected at random spends less than 12 months to buy a home?

# 6)

What proportion of buyers selected at random spends between 10.2 and 11.6 months to buy a home?

# 7)

What is the probability that it takes more than a year and a half to buy a home?

# 8)

Toby’s Trucking Company determined that the distance for traveled per truck per year is normally distributed, with a mean of 52 thousand miles and a standard deviation of 11.8 thousand miles.

a) What is the proportion of trucks that can be expected to travel either between 34 and 50 thousand miles?

b) What is the percentage of trucks that can be expected to travel below 38 thousand miles a year?

c) What is the proportion of trucks that can be expected to travel above 50 thousand miles a year?

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