Statistics and Probability Answers

The Office for admission of Hero Academy found out the IQ of incoming 1,200 freshmen normally distributed with a mean of 108 and a standard deviation of 10. They make a table to interpret their IQ.

You have a deck of 52 playing cards
(i) How many different 5 card hands can be dealt?
(ii) What is the probability that a hand of 5 dealt randomly contains 3 aces?
(iii) What is the probability that a hand of 5 dealt randomly will have 5 cards of the same
suit?

Suppose you have 9 different (distinguishable) coins, and 4 different (distinguishable) jukebox
slots.
(i) How many ways can you insert the 9 coins into the jukebox slots, if the order in which
the coins are inserted does not matter?
(ii) How many ways can you insert the 9 coins into the jukebox slots, if the order in which
the coins are inserted into each jukebox does matter?
(iii) How many ways can you insert 6 of the coins into one of the jukebox slots, if the order
in which the coins are inserted matters?

A random variable is normally distributed with a mean of 20 and a standard deviation of 4. If an observation is randomly selected from the​ distribution,
a. What value will be exceeded 25​% of the​ time?
b. What value will be exceeded ​85% of the​ time?
c. Determine two values of which the smaller has 10​% of the values below it and the larger has 10​% of the values above it.
d. What value will 15​% of the observations be​ below?

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.

(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 1700g 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.

(3.3.13) The tallest living man at one time had a height of 244 cm. The shortest living man at that time had a height of 65.5cm. 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.

(3.3.11) Consider a value to be significantly low if its z score less than or equal to -2 or consider a value to be significantly high if its z score is greater than or equal to 2.
A data set lists weights​ (grams) of a type of coin. Those weights have a mean of 5.28353 g and a standard deviation of 0.06149 g. Identify the weights that are significantly low or significantly high.
What weights are significantly​ low? Select the correct answer below and fill in the answer​ box(es) to complete your choice.
A. Weights that are less than?
B. Weights that are between? and?
C. Weights that are greater than?

(3.3.9) Consider a value to be significantly low if its z score less than or equal to -2 or consider a value to be significantly high if its z score is greater than or equal to 2.
A test is used to assess readiness for college. In a recent​ year, the mean test score was 20.5 and the standard deviation was 4.9. Identify the test scores that are significantly low or significantly high.
What test scores are significantly​ low? Select the correct answer below and fill in the answer​ box(es) to complete your choice.
A. Test scores that are greater than?
B. Test scores that are between ? and?
C. Test scores that are less than?

The score of driving test has a normal distribution with mean 70 if given the standard deviation of sample is eight. A driving school's instructor claimed that if the candidate learned more than three hours per week, the mean score would be different than 70. A driving test was given to a random sample of 50 candidates with the mean score was 78.

a) state the null and alternative hypothesis
b) identify the type I error and type II error that correspond to the hypothesis above
c) test the claim at 5% level of significance