Question

The distribution of weights of MP3 players is normally distributed with a mean of 6 ounces and a standard deviation of 2.5 ounces. What is the probability that a randomly chosen MP3 player has a weight of less than 4 ounces? Round to four decimal places. Put a zero in front of the decimal point.

The distribution of weights of MP3 players is normally distributed with a mean of 6 ounces and a standard deviation of 2.5 ounces. 20% of MP3 players are less than what weight? Round to the nearest hundredth

Answer 1

Solution :

Given that ,

mean = = 6

standard deviation = = 2.5

P(x < 4) = P[(x - ) / < (4 - 6) / 2.5]

= P(z < -0.8)

= 0.2119

Probability = 0.2119

mean = = 6

standard deviation = = 2.5

Using standard normal table ,

P(Z < z) = 20%

P(Z < -0.84) = 0.2

z = -0.84

Using z-score formula,

x = z * +

x = -0.84 * 2.5 + 6 = 3.9

weight 3.90