# mathematics

1.Medelian genetics. When Mendel conducted his famous genetic experiments with peas, one sample of offspring consisted of 580 peas, and Mendel theorized that 25 % of them would be yellow peas.

a. If Mendel’s theory is correct, find the mean and standard deviation for the number of yellow peas in such groups of 580 offspring peas.

b. The actual results consisted of 152 yellow peas. Is the result unusually high? What does this result suggest about Mendel’s theory?

2. Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. For a randomly selected adult, find the indicated probability or IQ score. Round scores to the nearest whole number(hint draw a graph in each case)

a. find the probability that a randomly selected adult has an IQ between 110 and 120 ( referred to as bright normal.)

3. Use the information about overhead reach distance of adult females. m=205.5 cm, Q=8.6 cm, and overhead reach distance are normally distributed. The overhead reach distance are used in planning assembly work stations.

a. If an adult female is randomly selected, find the probability that her overhead reach is between 180 cm and 200 cm.

b. If 50 adult females are randomly selected, find the probability that they have a mean overhead reach between 198 cm and 206 cm.

4. If the requirements of np is greater than or equal to 5 and nq is greater than or equal to 5 are both satisfied, estimate the indicated probability using the normal distribution as an approximation to the binomial distribution, if np is less than 5 or nq is less than 5, then that normal approximation should not be used.

a. with n=25 and p=0.4 find P(more than 9)