Question

NORMAL DISTRIBUTION

1A.

A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean of 58 months and a standard deviation of 4 months. Using the 68-95-99.7 rule, what is the approximate percentage of cars that remain in service between 66 and 70 months?

Do not enter the percent symbol.
ans =  %

1B.

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 45 ounces and a standard deviation of 10 ounces.

Use the Standard Deviation Rule, also known as the Empirical Rule.

Suggestion: sketch the distribution in order to answer these questions.

a) 95% of the widget weights lie between  and

b) What percentage of the widget weights lie between 15 and 65 ounces?  %

c) What percentage of the widget weights lie above 35 ?  %

1C.

If the distribution of weight of newborn babies in Maryland is normally distributed with a mean of 3.56 kilograms and a standard deviation of 0.68 kilograms, find the weights that correspond to the following z-scores. Round your answers to the nearest tenth, if necessary.

(a) z = -1.2

kilograms

(b) z = 0.94

kilograms

1D.

A doctor measured serum HDL levels in her patients, and found that they were normally distributed with a mean of 64.7 and a standard deviation of 3.6. Find the serum HDL levels that correspond to the following z-scores. Round your answers to the nearest tenth, if necessary.

(a) z = -1.25



(b) z = 1.54

1E.

The average resting heart rate of a population is 88 beats per minute, with a standard deviation of 13 bpm. Find the z-scores that correspond to each of the following heart rates. Round your answers to the nearest hundredth, if necessary.

(a) 116 bpm

z =

(b) 73 bpm

z =

1F.

The widths of platinum samples manufactured at a factory are normally distributed, with a mean of 1.2 cm and a standard deviation of 0.5 cm. Find the z-scores that correspond to each of the following widths. Round your answers to the nearest hundredth, if necessary.

(a) 2 cm

z =

(b) 1 cm

z =

Answer 1

Normal distribution:

1A. Here,

We need to find out

We also know that has a standard Normal.

When X=66,

When X=70,

Therefore by the properties of Normal curve.

We can look into tables to find the probailites:

  

Ans=2.15%

1B.

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 45 ounces and a standard deviation of 10 ounces.

Use the Standard Deviation Rule, also known as the Empirical Rule.

Suggestion: sketch the distribution in order to answer these questions.

a) 95% of the widget weights lie between  25.4 and 64.6
(Here Z=1.96, the limits are therefore
b) What percentage of the widget weights lie between 15 and 65 ounces? 97.59 %
  

  
c) What percentage of the widget weights lie above 35 ? 84.13 %

  

  

1C.

If the distribution of weight of newborn babies in Maryland is normally distributed with a mean of 3.56 kilograms and a standard deviation of 0.68 kilograms, find the weights that correspond to the following z-scores. Round your answers to the nearest tenth, if necessary.
We know that where
(a) z = -1.2

2.7 kilograms

(b) z = 0.94

4.2 kilograms

1D.

A doctor measured serum HDL levels in her patients, and found that they were normally distributed with a mean of 64.7 and a standard deviation of 3.6. Find the serum HDL levels that correspond to the following z-scores. Round your answers to the nearest tenth, if necessary.
We know that where
(a) z = -1.25
HDL=60.2

We know that   
(b) z = 1.54

HDL=70.2

1E.

The average resting heart rate of a population is 88 beats per minute, with a standard deviation of 13 bpm. Find the z-scores that correspond to each of the following heart rates. Round your answers to the nearest hundredth, if necessary.

Here,

We also know that

(a) 116 bpm

z =2.15

(b) 73 bpm

z =-1.15

1F.

The widths of platinum samples manufactured at a factory are normally distributed, with a mean of 1.2 cm and a standard deviation of 0.5 cm. Find the z-scores that correspond to each of the following widths. Round your answers to the nearest hundredth, if necessary.

Here,

We also know that

(a) 2 cm

z =1.6

(b) 1 cm

z =-0.4