6.

(a) Suppose it is known that 43% of Malawians own a Techno smartphone. If a random sample of 50 Malawians were surveyed, what is the probability that the proportion of the sample who owned a Techno smartphone is between 45% and 50%?

(b) One of the most famous large fractures in the earth's crust is the San Andreas Fault in California. A geologist attempting to study the movement of the earth's crust at a particular location found many fractures in the local rock structure. In an attempt to determine the mean angle of the breaks, she sampled 50 fractures and found the sample mean and standard deviation to be 39.8° and 17.2°, respectively.

i. Find the margin of error for estimating the population mean.

Probability Calculation: To find the probability of the proportion of Malawians owning Techno smartphones being between 45% and 50% in a sample of 50, you need to use the Normal distribution. First, calculate the standard error: sqrt((p(1-p))/n), where p is 0.43. Then find the z-scores for 45% and 50% and use a Z-table to find the probabilities.

Margin of Error Calculation: The margin of error for estimating the population mean is given by: z (standard deviation / sqrt(n)), where z is the critical value from the z-table for the desired confidence level.

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