# Question: The following is the distribution of the readings obtained with

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 = 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.

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

**View Solution:**## Answer to relevant Questions

The following are the hours of operation to failure of 38 light bulbs. Use a suitable statistical computer program to test whether the mean failure time of such light bulbs is significantly less than 300 hours. Use the 0.01 ...Show that if µY|x is linear in x and var(Y|x) is constant, then var(Y|x) = σ22 (1 – ρ2). Solve the normal equations on page 390 simultaneously to show that Use Theorem 4.15 show that Theorem 4.15 If X1, X2, . . . , Xn are random variables and Where a1, a2, . . . , an, b1, b2, . . . , bn are constants, then Use the formula for t of Exercise 14.28 to show that if the assumptions underlying normal regression analysis are met and β = 0, then R2 has a beta distribution with the mean 1 / n – 1. In exercisePost your question