Question

- WUL E IE EEEE .. 26. The table below shows the shoe-sizes of a normally distributed sample. If you found one pair of shoes that was size 9 (i.e., X-9), what proportion of the sample would be have feet too small to fit into the show (or in other words, what proportion of shoe sizes is smaller than a 9?) Descriptive Statistics Minimum Maximum Mean Std. Deviation 5.50 13.00 8.2386 1.53444 Shoe size Valid N (listwise) Answer: 27. The table below shows the number of siblings reported in a sample of students. What proportion of students in the sample have 4 or fewer siblings? Number of siblings Cumulative Percent Valid 0 9.1 Frequency Percent Valid Percent 9.1 9.1 34.1 34.1 29.5 29.5 43.2) 21 72.7 15.9 88.6 97.7 100.0 Total 100.0 100.0

Answer 1

26.
Let X be the shoe size of a randomly sampled person.
X ~ N(8.2386, 1.53444)
Proportion of people with shoe size less than 9 = P(X < 9) = P[Z < (9 - 8.2386) / 1.53444]
= P[Z < 0.50]
= 0.6915

27.
Proportion of students in the sample have 4 or fewer siblings = P(X $\le$ 4) = 97.7/100 (From Cumulative Percent)

= 0.977