Question

1. Data are drawn from a bell-shaped distribution with a mean of 160 and a standard deviation of 5. There are 1,400 observations in the data set.

a. Approximately what percentage of the observations are less than 170? (Round your answer to 1 decimal place.)
percentage of observations ______________%

b. Approximately how many observations are less than 170? (Round your answer to the nearest whole number.)
number of observations ______________

2. Data with 850 observations are drawn from a bell-shaped distribution with a mean of 72 and a standard deviation of 17. Approximately how many observations are more than 106? (Round your answer to the nearest whole number.)

Number of observations_______________

Answer 1

According to empirical rule,

i) Approximately 68% of the data fall within 1 standard deviations of thr mean.

ii) Approximately 95% of the data fall within 2 standard deviations of the mean.

iii) Approximately 99.7% of the data fall within 3 standard deviations of the mean.

Q.1) Given that, mean = 160

standard deviation = 5

Total observations = 1400

mean + 2 S.D. = 160 + (2 * 5) = 170

From empirical rule ii),

a) approximately, 2.5% + 95% = 97.5 % of the observations are less than 170.

b) expected observation that are less than 170 are,

1400 * 0.975 = 1365

Therefore, approximately 1365 observations are less than 170.

Q.2) Given that, mean = 72

standard deviation = 17

Total observations = 850

Mean + 2S.D.= 72 + (2 * 17) = 106

According to empirical rule ii), approximately 2.5% of the observations are more than 106

Expected observations that are more than 106 are,

850 * 0.025 = 21.25 ( approx 21)

Therefore, approximately 21 observations are more than 106