Question

From Excel spreadsheet below titled Price (A2:A351)    A) Produce a realtive frequency historgram for these data, does it seem plausible the data were sampled from a population that was normally distrubed? Determine the probabiltiy that a randomly chosen transaction would yeid a price of $2.12 or less even though the population mean was $2.51? Thanks very much.( FYI all the below numbers are less than 3 dollars/ its hard to see the period inbetween the dollars and cents)

Price

2.28

2.29

2.29

2.3

2.3

2.3

2.3

2.31

2.31

2.31

2.31

2.33

2.33

2.33

2.33

2.33

2.34

2.34

2.35

2.35

2.35

2.35

2.35

2.35

2.35

2.36

2.36

2.36

2.36

2.37

2.37

2.37

2.37

2.37

2.38

2.38

2.38

2.39

2.39

2.39

2.39

2.39

2.39

2.39

2.39

2.39

2.39

2.4

2.4

2.4

2.4

2.4

2.4

2.4

2.41

2.41

2.41

2.41

2.41

2.41

2.42

2.42

2.42

2.42

2.42

2.42

2.42

2.42

2.42

2.43

2.43

2.43

2.43

2.43

2.43

2.43

2.43

2.43

2.43

2.43

2.43

2.43

2.43

2.43

2.44

2.44

2.44

2.44

2.44

2.44

2.44

2.44

2.44

2.44

2.44

2.45

2.45

2.45

2.45

2.45

2.45

2.45

2.45

2.45

2.45

2.45

2.46

2.46

2.46

2.46

2.46

2.46

2.46

2.47

2.47

2.47

2.47

2.47

2.47

2.47

2.47

2.47

2.47

2.47

2.47

2.47

2.47

2.48

2.48

2.48

2.48

2.48

2.48

2.48

2.48

2.48

2.48

2.48

2.48

2.48

2.48

2.48

2.48

2.48

2.48

2.48

2.48

2.49

2.49

2.49

2.49

2.49

2.49

2.49

2.49

2.49

2.49

2.49

2.49

2.49

2.49

2.49

2.5

2.5

2.5

2.5

2.5

2.5

2.5

2.5

2.5

2.5

2.5

2.5

2.5

2.5

2.51

2.51

2.51

2.51

2.51

2.51

2.51

2.51

2.51

2.51

2.51

2.51

2.52

2.52

2.52

2.52

2.52

2.52

2.52

2.52

2.52

2.52

2.52

2.52

2.52

2.52

2.52

2.52

2.52

2.52

2.52

2.52

2.53

2.53

2.53

2.53

2.53

2.53

2.53

2.53

2.53

2.53

2.54

2.54

2.54

2.54

2.54

2.54

2.54

2.54

2.54

2.54

2.54

2.54

2.54

2.55

2.55

2.55

2.55

2.55

2.55

2.55

2.55

2.55

2.55

2.55

2.55

2.55

2.56

2.56

2.56

2.56

2.56

2.56

2.56

2.56

2.56

2.56

2.56

2.56

2.57

2.57

2.57

2.57

2.57

2.57

2.57

2.57

2.57

2.57

2.58

2.58

2.58

2.58

2.58

2.58

2.58

2.58

2.58

2.58

2.58

2.58

2.58

2.59

2.59

2.59

2.59

2.59

2.59

2.59

2.59

2.59

2.59

2.59

2.6

2.6

2.6

2.6

2.6

2.61

2.61

2.61

2.61

2.61

2.61

2.61

2.61

2.61

2.62

2.62

2.62

2.62

2.62

2.62

2.62

2.62

2.62

2.63

2.63

2.63

2.63

2.63

2.64

2.64

2.64

2.64

2.64

2.64

2.65

2.65

2.65

2.65

2.65

2.66

2.66

2.66

2.66

2.67

2.67

2.68

2.68

2.69

2.69

2.7

2.7

2.7

2.7

2.71

2.71

2.72

2.73

2.73

2.75

2.75

Answer 1

data is ={2013,4717,2666,4599,3810,4288,4701,3690,1684,5075,3984,5308,3018,2458,3344,2782,2546,2254,

1642,3439,3119,2089,3031,943,3505,6903,3412,3771,3450,2360,2929,3284,2563,2348,2555,4222,1804,

1603,2209,4676,4494,1894,2351,5387,2865,2569,3081,3917,4172,3959}

(a)

Yes,It is look like that it is sampled from normal distribution.

(b)

Mean =Σxi /50 =3269.66

variance = Σ(xi-mean) /49 =1180.636

(c)

P($2,000<x<$3,000)

=P($2,000-3269.66/1180.636<x-3269.66/1180.636<$3,000-3269.66/1180.636)

=P(-1.0754<z<-0.2284) = φ(-0.2284) - φ(-1.0754)

=0.40967 -0.14110 =0.26857

(d)

P($2,500<x)

=P($2,500-3269.66/1180.636<x-3269.66/1180.636)

=P(-0.652<z) =1- φ(-0.652)

=1-0.25720=0.7428