A wildlife reserve offers six types of annual membership to individuals. The charges are shown in the table below. Individual Membership Type Membership Charges per year,$ Friends of Bird Park 39 Friends of River Safari 65 Friends of the Zoo 105 Friends of Night Safari 105 Friends of Wildlife 145 Friends of Wildlife Plus 205 Of all the individuals who have taken up the annual membership, 20% hold Friends of Bird Park membership, 10% hold Friends of River Safari membership, 15% hold Friends of the Zoo membership, 25% hold Friends of Night Safari membership, 10% hold Friends of Wildlife membership and 20% hold Friends of Wildlife Plus membership. Assume no individual can hold more than one type of membership. The probability of observing the mean annual membership charges of a group of 30 members to be more than $105=______.Please fill in the blank.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...