The life spans of a species of fruit fly have a bell-shaped distribution, with a mean of 32 days and a standard deviation of 5 days. (a) The life spans of three randomly selected fruit flies are 37 days, 27 days, and 44 days. Find the z-score that corresponds to each life span. Determine whether any of these life spans are unusual. (b) The life spans of three randomly selected fruit flies are 22 days, 27 days, and 42 days. Using the Empirical Rule, find the percentile that corresponds to each life span.

(a) z score (37)  = 1

    z score (27) = -1

    z score (44)  = 2.4

(b) Ф(-2) = 1 - 0.97 = 3%

     Ф(-1) = 1 - 0.84 = 16%

     Ф(2) = 0.97 = 97%

Explanation:

Given -

Mean of life span = 32 days

Standard deviation of life span = 5 days

Life span of 3 random selected fruit flies are = 37, 27 and 44

(a) Z score = data point - mean / standard deviation

z score (37)  = 37 - 32 / 5 = 1

z score (27) = 27 - 32 / 5 = -1

z score (44) = 44 - 32 / 5 = 2.4

A positive z-score says the life span is above average.

A negative z-score says the life span is below average.

(b) Life span of 3 randomly selected fruit flies = 22, 27, 42

z score (1) = 22-32/5 = -2

z score (2) = 27-32/5 = -1

z score (3) = 42-32/5 = 2

From the z score table, the value of phi is taken

z(22) = -2

Ф(-2) = 1 - 0.97 = 3%

z(27) = -1

Ф(-1) = 1 - 0.84 = 16%

z(42) = 2

Ф(2) = 0.97 = 97%

d concave shape of wave rock

explanation:

the concave shape of wave rock is a very good evidence that supports the evolution of earth due to chemical weathering. if we talk about structure of   wave rock, studies have estimated that it is around 2.7 billion years old. it also serves as the foundation of evidence that it was the place where australian continent began to form.

how the structure of wave rock was created?

studies suggest that structure of wave rock was created when the surrounded area was started to weather due to which deposition of material started on the part of land which now contains wave rock.

the structure of wave rock is considered to be one of the best-known landforms in australia. at the height of around 15 cm, there can be found flared slopes which formulate the margins of hyden rock. it is now assumed by geologists that wave rock was created by subsurface water-induced weathering and not by glaciers, waves or wind.

due to deposition of material over the period of long time, the wave rock became tougher and tougher due to weathering from surrounding terrain. this makes it a physical evidence that supports   the evolution of earth due to chemical weathering.

hope it !

in the year 2850, humans successfully colonized mars. the martian modules that were constructed could hold only a small population of people. it is now a century later, and the population on mars has grown to 600 people. of the current mars population, 45 people express the recessive phenotype for phenylketon- uria (pku) syndrome (pp genotype).

explanation: