which two data sets appear to be normally distributed?\na. \n| value | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40…

which two data sets appear to be normally distributed?\na. \n| value | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 |\n| frequency | 10 | 27 | 40 | 60 | 75 | 100 | 80 | 55 | 35 | 30 | 11 |\nb. \n| value | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 |\n| frequency | 11 | 17 | 23 | 29 | 35 | 41 | 47 | 53 | 59 | 65 | 71 |\nc. \n| value | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 |\n| frequency | 12 | 25 | 32 | 41 | 68 | 75 | 66 | 52 | 35 | 26 | 13 |\nd. \n| value | 5 | 10 | 15 | 20 | 25 | 30 | 21 | 24 | 27 | 30 | 33 |\n| frequency | 13 | 18 | 23 | 28 | 33 | 38 | 43 | 48 | 53 | 58 | 63 |

which two data sets appear to be normally distributed?\na. \n| value | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 |\n| frequency | 10 | 27 | 40 | 60 | 75 | 100 | 80 | 55 | 35 | 30 | 11 |\nb. \n| value | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 |\n| frequency | 11 | 17 | 23 | 29 | 35 | 41 | 47 | 53 | 59 | 65 | 71 |\nc. \n| value | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 |\n| frequency | 12 | 25 | 32 | 41 | 68 | 75 | 66 | 52 | 35 | 26 | 13 |\nd. \n| value | 5 | 10 | 15 | 20 | 25 | 30 | 21 | 24 | 27 | 30 | 33 |\n| frequency | 13 | 18 | 23 | 28 | 33 | 38 | 43 | 48 | 53 | 58 | 63 |

Answer

Explanation:

Step1: Recall normal - distribution property

A normal - distribution has a symmetric frequency distribution around the mean. The frequencies increase to a maximum at the mean and then decrease symmetrically.

Step2: Analyze Option A

The frequencies in Option A: 10, 27, 40, 60, 75, 100, 80, 55, 35, 30, 11. The frequencies increase from 10 to 100 and then decrease in a somewhat symmetric fashion around the value of 30 (where the frequency is 100).

Step3: Analyze Option C

The frequencies in Option C: 12, 25, 32, 41, 68, 75, 66, 52, 35, 26, 13. The frequencies increase from 12 to 75 and then decrease in a relatively symmetric way around the value of 30 (where the frequency is 75).

Step4: Analyze Option B

The frequencies in Option B: 11, 17, 23, 29, 35, 41, 47, 53, 59, 65, 71. The frequencies are increasing in a linear - like fashion and do not show the symmetric bell - shape of a normal distribution.

Step5: Analyze Option D

The values in Option D have some irregularities in the sequence of values (21, 24, 27) and the frequencies do not show a symmetric pattern around a central value.

Answer:

A. value 5 10 15 20 25 30 35 40 45 50 55, frequency 10 27 40 60 75 100 80 55 35 30 11; C. value 5 10 15 20 25 30 35 40 45 50 55, frequency 12 25 32 41 68 75 66 52 35 26 13