(1 point) in a study of retention rates of those using the platinum program at jenny craig in may 2001-may 2002, it was found that about 25%25% of those who began the program dropped out in the first four weeks. if we have a random sample of 246 people at the beginning of the program, what is the probability that at least 195 people in the sample will still be in the platinum program after the first four weeks?

The required probability is calculated as 0.052

Solution:

As per the question:

The probability that people dropped out in the first 4 weeks of the program, p = 0.25

The size of the sample, n = 246

Now,

To calculate the Probability of at least 195 people being in the program after first 4 weeks:

              (1)

where

= mean

= standard deviation

X = No. of people still part of the program

Now,

Mean can be given as:

The mean no. of people still part of the program = 246 - 62 = 184

Standard deviation is given by:

where

q = 1 - p = 1 - 0.25 = 0.75

Now, using the appropriate values in eqn (1):

= 1 - P(Z < 1.62)

Using Z-table:

Thus the required probability is calculated as 0.052

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.