Question

In: Statistics and Probability

Pease answer the questions below: If n = 15, ¯xx¯ = 50, and s = 15,...

Pease answer the questions below:

  1. If n = 15, ¯xx¯ = 50, and s = 15, construct a confidence interval at a 95% confidence level. Assume the data came from a normally distributed population. Give your answers to three decimal places.

    < μ <
  1. 55 randomly selected students were asked the number of pairs of shoes they have. Let X represent the number of pairs of shoes. The results are as follows:

# of Pairs of Shoes

4

5

6

7

8

9

10

Frequency

7

8

4

11

8

9

8



Round all your answers to 4 decimal places where possible.

The mean is: Incorrect

The median is: Correct

The sample standard deviation is: Incorrect

The first quartile is: Correct

The third quartile is: Correct

What percent of the respondents have at least 6 pairs of Shoes? Incorrect%

35% of all respondents have fewer than how many pairs of Shoes?

  1. Based on historical data, your manager believes that 25% of the company's orders come from first-time customers. A random sample of 114 orders will be used to estimate the proportion of first time-customers. What is the probability that the sample proportion is less than 0.29?

    Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations.

    Answer =  (Enter your answer as a number accurate to 4 decimal places.)



    Solutions

    Expert Solution

    a) Given, n = 15, mean = 50, S = 15.

    95% confidence interval is given by,

      

    C.I = ( 41.69, 58.31)

    b)

    # of pairs Frequency C.F rel. Freq c.rel. F Xf (X-xbar)2 f
    4 7 7 0.13 0.13 28 70.076272
    5 8 15 0.15 0.28 40 37.463168
    6 4 19 0.07 0.35 24 5.419584
    7 11 30 0.2 0.55 77 0.295856
    8 8 38 0.15 0.7 64 5.591168
    9 9 47 0.16 0.86 81 30.338064
    10 8 55 0.14 1 80 64.343168
    Total 55 1 394 213.52728

    Mean is,

    = 394/55 = 7.164

    Median is,

    M = (55+1)/2 th value

    = 28th value = 7

    Sample standard deviation is,

    First Quartile,

    Q1 = (n+1)/4 th value = 14th value = 5

    Third Quartile,

    Q3 = 3(n+1)/4 th value = 42 nd vaue = 9

    The percentage of the respondents have at least 6 pairs of Shoes,

    = 1 - 0.28 = 0.72

    35% of all respondent have fewer than 6 pairs of shoes.

    c) A manager believes that 25% of the company's orders come from first-time customers. A random sample of 114 orders will be used to estimate the proportion of first time-customers.

    n = 114, p = 0.25

    The probability that the sample proportion is less than 0.29,

    = 0.8380(ans)

    ****If you have any queries or doubts please comment below. if you're satisfied please give a like. Thank you!


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