Question

In a recent​ survey, a media research company determined the cost of extra​ high-definition (HD) gear required to watch television in HD. The costs ranged from​ $5 a month for a​ set-top box to​ $200 for a new satellite. The full results of the survey are shown below. Assume that the population average cost is​ $150 and the standard deviation is​ $50.

HD_Equipment_Costs

117.23

166.18

160.17

140.93

41.64

79.83

99.51

151.23

197.52

169.53

66.8

89.9

141.77

188.59

182.99

131.96

100.89

63.05

115.12

145.54

204.96

168.54

157.38

152.96

74.79

208.04

93.36

138.92

67.66

195.1

62.63

167.16

98.56

214.11

231.63

238.4

201.04

209.04

134.04

59.72

207.57

104.96

213.62

229.57

227.76

82.11

170.27

100.53

239.94

208.48

200.93

81.31

110.13

47.18

133.53

92.66

168.92

202.46

188.87

146.68

183.2

115.37

129.76

68.6

80.44

217.77

84.15

149.18

87.97

139.64

160.61

87.83

125.39

122.44

180.57

95.89

46.11

82.72

233.68

245.37

47.32

100.73

52.26

145.97

175.86

124.11

155.29

64.14

145.7

174.52

205.52

169.02

169.96

100.33

185.78

98.8

127.94

149.32

187.39

173.76

180.48

138.63

85.63

189.99

167.39

68.16

152.4

70.06

87.89

179.69

100.2

160.35

116

91.12

140.43

184.6

262.14

184.43

64.26

110.44

100.44

145.12

104.61

134.74

104.82

156.66

149.6

154.61

84.3

91.97

153.54

157.06

142.48

150.79

131.78

157.62

155.81

127.99

192.42

190.54

199.14

125.51

122.39

222.44

138.15

132.34

141.64

152.48

149.29

219.92

Could this population be normally​ distributed?

A. No. The box and whisker​ plot's median is too far from the claimed population mean.

B. It is not possible to determine whether the population is normally distributed using the box and whisker plot.

C. No. The box and whisker plot is not symmetrical.

D. Yes. The box and whisker plot is nearly symmetrical and drops off sharply as distance from the median​ increases, and the median is near the claimed population mean.

​b) Determine the probability that the mean of a random sample of 150 costs for HD extras would be more than ​$7 away from the mean of the sample described above.

The probability is ________.

​(Round to four decimal places as​ needed.)

​c) Given your response in part​ a, is it possible for the results in part b to be​ valid?

A. ​No, because the population cannot be normally distributed.

B. ​Yes, because the Central Limit Theorem guarantees that the sampling distribution of sample means is normally distributed given a large sample size.

C. There is not enough information to determine whether the results from the previous section are valid.

D. ​No, because the sample size is too small for the Central Limit Theorem to apply.

Answer 1

Population Mean, M = 150

Population Standard Deviation, S = 50

Given Sample data has 150 observations

Sample Mean, x = 142

The box-whisker plot for the sample data is as follows-

a) Yes. The box and whisker plot is nearly symmetrical and drops off sharply as the distance from the median increases, and the median is near the claimed population mean.

This will be Option-(D)

b) P(135<X<149)

For 135, Z1 = (135-150)/50 = -0.3

For 149, Z2 = (149-150)/50 = -0.02

P(-0.3<Z<-0.02) = P(Z<-0.02) - P(Z<-0.3) = 0.4920 - 0.3821 = 0.1099

c) Yes, because the Central Limit Theorem guarantees that the sampling distribution of sample means is normally distributed given a large sample size.

This will be (B)

Let me know if you need anything else, if not please don't forget to like the answer :)