Focus groups of 12 people are randomly selected to discuss p

Focus groups of 12 people are randomly selected to discuss products of the Yummy Company. It is determined that the mean number (per group) who recognize the Yummy brand name is 9.4 and the standard deviation is 0.98. Would it be unusual to randomly select 12 people and find that fewer than 5 recognize the Yummy brand name?

yes or no ?

would you please show work so i can understand how did you find out the answer ?

Solution

population mean,u = 8.5
standard deviation,sigma = 0.98

P(X< 5 ) = P(Z< ((5-8.5) / 0.98)
= P(Z< -3.57 )
= 1 - P(Z<3.57)
= 1 - 0.9998
= 0.0002

Since probability is very small (almost 0) hence it is unusual to randomly select 12 people and find that fewer than 5 recognize the yummy brand name.