Question

Good morning,

I'm having trouble solving these, any chance for guidance?

(b) Three friends, Helga, Amelie and Sun, regularly meet at a caf ́e. Based on previous experience, the probability that Helga buys a slice of cake
is 0.45, the probability that Amelie buys a slice of cake is 0.38, and the probability that Sun buys a slice of cake is 0.70. What is the probability that all three buy a slice of cake the next time they visit the caf ́e? State any important assumption that you make in order to calculate this probability.

The normal distribution of a variable x has mean μ = −1 and
standard deviation σ = 0.5.

2. (ii) Write down the formula for z that converts each value of the
   variable x in part (b)(i) to the number of standard deviations from
   its mean. Your formula should be written down in a form that does
   not involve any fraction or decimal.

3. (iii) Calculate the value of z corresponding to x = −1.8. Interpret the
   value of z in terms of the number of standard deviations x is above
   or below its mean.

4. (c) Emails sent internally within a large organisation may or may not have extra files associated with them as ‘attachments’. Consider only emails that have a single attachment. Suppose that the population distribution of the sizes of such attachments has a mean of 0.95 megabytes (MB) and a standard deviation of 0.4 MB.

   (i) Find the standard deviation of the sampling distribution of the
   mean for samples of 30 such attachments.

   (ii) Hence give the approximate distribution of the sample mean for samples of 30 such attachments.

Thank you ?

Answer 1