The following is the distribution of the readings obtained with a Geiger counter of the number of particles emitted by a radioactive substance in 100 successive 40-second intervals:

(a) Verify that the mean and the standard deviation of this distribution are x̅ = 20 and s = 5.

(b) Find the probabilities that a random variable having a normal distribution with µ = 20 and σ = 5 will take on a value less than 9.5, between 9.5 and 14.5, between 14.5 and 19.5, between 19.5 and 24.5, between 24.5 and 29.5, between 29.5 and 34.5, and greater than 34.5.

(c) Find the expected normal curve frequencies for the various classes by multiplying the probabilities obtained in part (b) by the total frequency, and then test at the 0.05 level of significance whether the data may be looked upon as a random sample from a normal population.

Transcribed Image Text:

of Fquency particles 5-9 10-14 15-19 20-24 25-29 30-34 35-39 10 37 36 13