Area Under Normal Curve Worksheet Answers

Area Under Normal Curve Worksheet Answers

Assume that is normally distributed with a specified mean and standard deviation. Find the indicated probabilities :

Find the described and sketch the area on the given curve.

1. Find such that 6% of the standard normal curve lies to the left of

6% = 0.0600

From the table z = -1.55 at 0.0606

z = -1.56 at 0.0594

Right in between so

1. Find such that 55% of the standard normal curve lies to the left of

55% = 0.5500

From the table z = 0.12 at 0.5478

Z = 0.13 at 0.5517

0.5500 is closer to 0.5517 so

1. Find such that 8% of the standard normal curve lies to the right of

8% to the right = 1 – 0.0800 = 0.9200

From the table z = 1.40 at 0.9192

z = 1.41 at 09207

0.9200 is closer to 0.9207 so

1. Find such that 95% of the standard normal curve lies to the right of

95% to the right = 1 – 0.9500 = 0.0500

From the table z = - 1.64 at 0.0505

z = - 1.65 at 0.0495

Right in between so

1. Find such that 98% of the standard normal curve lies between

From the table z = - 2.32 at 0.0102

z = - 2.33 at 0.0099

0.0100 is closer to 0.0099 so

98% of the data will fall between

1. Find such that 60% of the standard normal curve lies between

From the table z = - 0.84 at 0.2005

z = - 0.85 at 0.1977

0.2000 is closer to 0.2005 so

60% of the data will fall between

1. A person’s blood glucose level and diabetes are closely related. Let be a random variable measured in milligrams of glucose per deciliter of blood. After a

12 – hour fast, the random variable will have a distribution that is approximately normal with a mean and a standard deviation After 50 years, these tend to increase. Find the probability that, an adult under 50 years of age after a

12 – hour fast will have :

a)

b)

( from the table )

c)

** z – scores from above

1. Quick Start makes 12 – volt car batteries. After many years of product testing, the company knows the average life of a Quick Start battery is normally distributed, with a mean of 45 months and a standard deviation of 8 months.

a) If Quick Start fully refunds any batteries that fail within a 36 – month period of purchase, what percentage of batteries will the company expect to replace ?

The company will expect to replace 13% of the batteries

b)If Quick Start does not want to make refunds for more than 10% of its batteries under full – refund guarantee policy, for how long should the company guarantee the batteries ? ( round to nearest month )

10% = 0.1000 which coverts to

The company should guarantee their batteries for 35 months

1. Do the following data sets have a normal curve ? Use Person’s index.

a) Mean = 30.2 , standard deviation = 1.8 , median = 30

Data has a normal curve --- index value falls between -1 and 1

b) Mean = 134.3 , standard deviation = 40.6 , median = 150

Data does not have a normal curve --- index value falls outside -1 to 1

c) Mean = 86 , standard deviation = 6.2 , median = 84

Data has a normal curve --- index value falls between -1 and 1