Statistics and Probability Answers

1) Given the mean weight of 60 kg with a standard deviation of 5 kg among students in college this school year at University X, describe the in general the composition of the population of students in terms of weight.

(3.3.13) The tallest living man at one time had a height of 244 cm. The shortest living man at that time had a height of 65.5 cm. Heights of men at that time had a mean of 172.29 cm and a standard deviation of 7.64 cm. Which of these two men had the height that was more​ extreme?

Since the z score for the tallest man is z=? and the z score for the shortest man is z=?​, the tallest/shortest man had the height that was more extreme

(3.3.15) Based on sample​ data, newborn males have weights with a mean of 3243.4 g and a standard deviation of 574.9 g. Newborn females have weights with a mean of 3025.6 g and a standard deviation of 724.6 g. Who has the weight that is more extreme relative to the group from which they​ came: a male who weighs 1700 g or a female who weighs 1700 ​g?

Since the z score for the male is z=? and the z score for the female is z=?​, the female/male has the weight that is more extreme.

(3.3.16) In a recent awards​ ceremony, the age of the winner for best actor was 32 and the age of the winner for best actress was 50. For all best​ actors, the mean age is 41.3 years and the standard deviation is 5.4 years. For all best​ actresses, the mean age is 35.3 years and the standard deviation is 10.2 years.​ (All ages are determined at the time of the awards​ ceremony.) Relative to their​ genders, who had the more extreme age when winning the​ award, the actor or the​ actress? Explain.
Since the z score for the actor is z ? and the z score for the actress is z=?​, the actress/actor had the more extreme age

A class consists of 100 students, 60 students like music, 70 students like football,
and 30 students like football and music. A student is chosen randomly, what is
the probability that:
a. He likes music only.
b. He doesn't like music or football.
c. He doesn't like music and football.

Assume that a real estate manager has 5 contacts per week, and she believes that for each contact
the probability of making a sale is 0.30. Calculate the following if possible. If any part of question
(you feel) is not possible to calculate give reason:
a. Develop the probability distribution table for sale
b. Calculate the expected number of sales per week and variance of sale
c. Find the probability that she makes at most 2 sales.
d. Find the probability that she makes between 3 and 6 sales (both inclusive).

(5.2.15) Assume that a procedure yields a binomial distribution with n=5 trials and a probability of success of p=0.50. Use a binomial probability table to find the probability that the number of successes x is exactly 2.
P(2)=

(5.1.15) Refer to the accompanying​ table, which describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Find the mean and standard deviation for the number of girls in 8 births.
Number of
Girls x ​P(x)
0 0.006
1 0.035
2 0.109
3 0.222
4 0.277
5 0.213
6 0.107
7 0.026
8 0.005
The mean is mu ? ​girl(s)

(5.1.16) The accompanying table describes results from groups of 10 births from 10 different sets of parents. The random variable x represents the number of girls among 10 children. Use the range rule of thumb to determine whether 1 girl in 10 births is a significantly low number of girls.
Number of
Girls x P(x)
0 0.003
1 0.016
2 0.036
3 0.112
4 0.208
5 0.233
6 0.199
7 0.115
8 0.042
9 0.012
10 0.024
Use the range rule of thumb to identify a range of values that are not significant.
The maximum value in this range is ?? girls.