A market survey was conducted to estimate the proportion of homemakers who would recognize the brand name of a cleanser based on the shape and the colour of the container. Of the 1400 homemakers sampled, 420 were able to identify the brand by name.

a. Estimate the value of the population proportion.

b. Estimate the value of the standard error of proportions.

c. What is the probability that less than 390 homemakers would recognize the brand name of a cleanser based on the shape and the colour of the container?