Question

1) Find the probability using the standard normal distribution.

a) 0.5900 b) 0.3409 c) 0.8409 d)0.6591

2) Find the z value that corresponds to the given area.

3) The length of country and western songs is normally distributed and has a mean of 170 seconds and a standard deviation of 20 seconds. Find the probability that a random selection of 16 songs will have mean length of 164.15 seconds or less. Assume the distribution of the lengths of the songs is normal.

a) 0.88 b)0.12 c)0.38 d)0.62

Answer 1

Solution :

Given that ,

mean = = 170

standard deviation = = 20

n = 16

= 170

=  / n = 20 / 16=5

P( < 164.15) = P[( - ) / < (164.15 -170) / 5]

= P(z < -1.17)

Using z table  

= 0.1210

probability=0.12