Question

79.2 78.11 79.18 80.32 82.05 82.57 82.88 83.83 85.35 84.79 85.79 86.36 87.01 88.64 87.73 87.64 87.93 87.85 87.01 87.57

84.5905 =AVERAGE 3.369434554 =Standard deviation .

. Use Excel to calculate the average and standard deviation of the close data column. Assume that these two numbers represent the population (=parametric) mean and population standard deviation, respectively, for the variable length (in cm) in a population of a species of fish. Attach a printout of the data to your homework and write down the ticker code on it.

a. Calculate the probability of sampling at random a fish that is smaller in size than the value you would obtain by subtracting half the standard deviation from the average [x will be equal to: μ – (σ/2)]

b. Calculate the probability of sampling at random a fish that is greater in size than the value you would obtain by adding half the standard deviation from the average [x = μ + (σ/2)]

c. Calculate the probability of sampling at random a fish that has a size between the two values [x = μ – (σ/2), x = μ + (σ/2)] used in parts “a” and “b,” respectively

d. Calculate the 25th and 75th percentiles of fish size for the population using the normal distribution table.

e. Imagine that 5 individuals are sampled at random from this fish population. Calculate the probability that the average calculated will be less than the value: μ – (σ/3)

NOTE: Assume the variable is normally distributed and use bell-shaped curve diagrams to shade the areas that correspond with the answers to questions “a” through “d” that is the data set i have given above. please show full working

Answer 1

Solution:

Mean =

S.D.(s) =

a)

Value of z to the left of z =-0.5 (from the z table) = 0.3085

b)

Required probability= 1- (Value of z to the left of 0.5)

= 1-.6915= 0.3085

c) probability that a random fish has a size between and

= 0.6915 - .3085 = 0.283

d)

Value of z at 25th percentile = - 0.6744

Value of z at 75th percentile= 0.6744

(Value of z found using the z table)

Value of x at 25th percentile

X= 82.33

Value of x at 75th percentile

X= 86.87