Question

According to the American music industry, the length of a song is normally distributed with a mean of 240 seconds and standard deviation thirty seconds. Suppose a random sample of fifteen songs is selected from the morning program. what is the probability that the length of the song is between 225 and 260 seconds long?​

Answer 1

96.89%

Explanation:

Find the standard error:

s = σ/√n

s = 30 / √15

s = 7.75

Find the z-scores:

z = (x − μ) / s

z₁ = (225 − 240) / 7.75

z₁ = -1.94

z₂ = (260 − 240) / 7.75

z₂ = 2.58

Find the probability.

P(-1.94 < Z < 2.58) = P(Z<2.58) − P(Z<-1.94)

P(-1.94 < Z < 2.58) = 0.9951 − 0.0262

P(-1.94 < Z < 2.58) = 0.9689