Standard Deviation Binom

Standard Deviation Binom

PHS

NOTE: R is not required for this assignment. You can use a calculator or R to help you
with calculations.

  1. In a particular population, it was determined that the distribution of 5-year old children’s heights (X) was normally distributed, with a mean µ = 99 cmand standard deviation ó = 7 cm.
    a. What is P(X < 99 cm)?
    b. What is P(X ≤ 99 cm)?
    c. What is P(86 cm < X < 101 cm)?
    d. What percentage of 5-year old children in this population has a heightgreater than 105 cm?
    e. What is the height in this population that represents the 85thpercentile, i.e., the height such that 85% of the heights are less than it? (Hint:start by finding a z-score).
    2. Let X = the number of traffic accidents to occur in a given day on aparticular road. The probability distribution of X appears in the following table.
    (NOTE: we are not assuming X follows any particular (named) probabilitydistribution.):
x 0 1 2 3 4 ≥ 5
P(X=x) .15 .28 .25 .19 .10 .03
  1. What is the probability that at least two traffic accidents occur in agiven day on this road?
    b. What is the probability that at most two traffic accidents occur in agiven day on this road?
    c. What is the probability of greater than three accidents occurring on agiven day on this road?
    d. What is the probability of three or greater accidents occurring on agiven day on this road?
    e. From this table, can you determine the probability of exactly 5accidents occurring on a given day on this road? Briefly explain your answer.
    f. Though you are told above that the distribution of X does not comefrom a named distribution, given the nature of the data what do you think wouldbe the most logical distribution that X might follow? Briefly explain your answer.
    3. A questionnaire study was conducted and it was observed that the“activity” that airline passengers like to engage in the most is to sleep. In fact,60% of respondents to a survey chose this activity over others. For the purposesof this problem, assume the survey respondents came from a random sample of allairline passengers. Now, assume we speak to 10 random people from thispopulation who are just about to board a large flight, and we know that these
    people do not know one another. Let X = the number of people from these 10who say they would, of all activities, prefer to sleep on the plane. Here, then, wecan assume X ~ Binom(n = 10, p=.60).
    a. What is P(X = 6)?
    b. What is P(X = 6)c?
    c. What is P(X ≤ 4)?
    d. What is P((X = 3) or (X=7))?
    e. What is the probability that more than half the interviewed passengerswould prefer to sleep?

Solution