The average diameter of sand dollars on a certain island is 4.00 centimeters with a standard deviation of 0.60 centimeters. If 16 sand dollars are chosen at random for a collection, find the probability that the average diameter of those sand dollars is more than 3.85 centimeters. Assume that the variable is normally distributed.

0.8413 is the required probability.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 4.00 centimeters

Standard Deviation, σ = 0.60 centimeters

Sample size, n = 16

We are given that the distribution of average diameter is a bell shaped distribution that is a normal distribution.

Formula:

Standard error due to sampling =

P(diameter of sample is more than 3.85 centimeter)

P(x > 3.85)

Calculation the value from standard normal z table, we have,  

0.8413 is the probability that the  the average diameter of sample of 16 sand dollars is more than 3.85 centimeters.

answer: first option i.e. 'a' is correct.

step-by-step explanation:

since we have given that

number of minutes to wrap a small gift box = 4 minutes

we need to find the number of gifts to be wrapped in 5 minutes

since there is a direct variation, as the number of minutes will increase with   number of gifts to be wrapped.

so, let the number of gifts to be wrapped in 5 minutes be x.

so, it becomes,

hence, first option 'a'   is correct.