The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 246.8 and a standard deviation of 67.2. (All units are 1000 cells/μL.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 1 standard deviation of the mean, or between 179.6 and 314.0? b. What is the approximate percentage of women with platelet counts between 45.2 and 448.4?

a. 68%

b. 99.7%.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 246.8

Standard deviation = 67.2

a. What is the approximate percentage of women with platelet counts within 1 standard deviation of the mean, or between 179.6 and 314.0?

By the Empirical Rule, approximately 68%.

b. What is the approximate percentage of women with platelet counts between 45.2 and 448.4?

45.2 = 246.8 - 3*67.2

448.4 = 246.8 + 3*67.2

Within 3 standard deviations of the mean, so approximately 99.7%.

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.

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