Question

The mass of a species of mouse commonly found in houses is normally distributed with a mean of 19.7 grams with a standard deviation of 0.13 grams. Enter your responses as a decimal with 4 decimal places.

What is the probability that a randomly chosen mouse has a mass of less than 19.55 grams?

What proportion of mice have a mass between 19.59 and 19.8 grams?

25% of all mice have a mass of less than  grams.

Answer 1

Solution :

Given that ,

P(x < 19.55) = P[(x - ) / < (19.55 - 19.7) / 0.13]

= P(z < -1.15)

= 0.1251

Probability = 0.1251

P(19.59 < x < 19.8) = P[(19.59 - 19.7)/ 0.13) < (x - ) /  < (19.8 - 19.7) / 0.13) ]

= P(-0.85 < z < 0.77)

= P(z < 0.77) - P(z < -0.85)

= 0.7793 - 0.1977

= 0.5816

Proportion = 0.5816

Using standard normal table ,

P(Z < z) = 25%

P(Z < -0.67) = 0.25

z = -0.67

Using z-score formula,

x = z * +

x = -0.67 * 0.13 + 19.7 = 19.6129

19.6129 grams