Question

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 <

2. 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?

3. 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.)

Answer 1

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)

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