The weight of a soccer ball is normally distributed with a mean of 0.43 kg and a standard deviation of 0.01 kg.

Suppose 800 different soccer balls are in a warehouse.

About how many soccer balls weigh more than 0.45 kg?

12

20

24

40

Times for an ambulance to respond to a medical emergency in a certain town are normally distributed with a mean of 450 seconds and a standard deviation of 50 seconds.

Suppose there are 97 emergencies in that town.

In about how many emergencies are the response times expected between 400 seconds and 500 seconds?

31

33

47

66

jbouyer Mar 13, 2018

#1**0 **

≈≈≈Soccer balls:

Number of standard deviations above the mean = (0.45 - 0.43)/0.01 → 2

A proportion of ≈ 0.023 lie above 2 standard deviations (from tables)

0.023*800 ≈ 18

Ambulances:

Stdevs below mean = (400 - 450)/50 = -1

Stdevs above mean = (500 - 450)/50 = 1

Proportion between these: 0.843 - (1-0.843) = 0.686

Expect 0.686*97 = 67

Alan Mar 13, 2018

#2**0 **

Hi

the generally accepted 3 sigma values are 68%,95% and 99.7%. These are only approximate and so may vary slightly from school to school.

what it means is the coverage of scores within 1 s.d. of the mean is 68%, within 2 s.d. Is 95% and 99.7% within 3 s.d.

answer one is 20 ie 2.5% of 800

answer two is 67 ie within 1 s.d. of the mean or 68% of 97

Guest Mar 14, 2018