Question

A normally distributed population of lemming body weights has a mean of 63.5 g and a standard deviation of 12.2 g.

1. What proportion of this population is 43.0g or smaller?

2. If there are 1000 weights in the population, how many of them are 43.0 or smaller?

3. What is the probability of a body weight between 50.0 and 60.0 g?

Answer 1

Solution :

Given that ,

mean = = 63.5

standard deviation = = 12.2

i.

P(x 43.0)

= P[(x - ) / (43.0 - 63.5) / 12.2]

= P(z -1.68)

= 0.0465

proportion = 0.0465

ii.

P(x 43.0)

= P[(x - ) / (43.0 - 63.5) / 12.2]

= P(z -1.68)

= 0.0465

= 1000 * 0.0465 = 46.5

Answer = 46.5

iii.

P(50.0 < x < 60.0) = P[(50.0 - 63.5)/ 12.2) < (x - ) /  < (60.0 - 63.5) / 12.2) ]

= P(-1.11 < z < -0.29)

= P(z < -0.29) - P(z < -1.11)

= 0.3859 - 0.1335

= 0.2524

Probability = 0.2524