A chain of stores wishes to build customer loyalty by offering gift vouchers to its privileged customers. Each of them receives a gift voucher of green or red colour on which an amount is written. Gift vouchers are distributed so as to have, in each store, one quarter of red vouchers and three quarters of green vouchers. Green gift vouchers take the value of 30 euros with a probability equal to 0.067 or values between 0 and 15 euros with unspecified probabilities here. Similarly, red gift vouchers take the values 30 or 100 euros with probabilities respectively equal to 0.015 and 0.010 or values between 10 and 20 euros with unspecified probabilities here. In one of the stores of this chain, out of 200 privileged customers, 6 received a gift voucher with a value greater than or equal to $30 €$. The manager of the store in question believes that this number is insufficient and doubts the random distribution of gift vouchers in the different stores of the chain. Are his doubts justified?
A chain of stores wishes to build customer loyalty by offering gift vouchers to its privileged customers. Each of them receives a gift voucher of green or red colour on which an amount is written.\\
Gift vouchers are distributed so as to have, in each store, one quarter of red vouchers and three quarters of green vouchers.\\
Green gift vouchers take the value of 30 euros with a probability equal to 0.067 or values between 0 and 15 euros with unspecified probabilities here.\\
Similarly, red gift vouchers take the values 30 or 100 euros with probabilities respectively equal to 0.015 and 0.010 or values between 10 and 20 euros with unspecified probabilities here.
In one of the stores of this chain, out of 200 privileged customers, 6 received a gift voucher with a value greater than or equal to $30 €$.
The manager of the store in question believes that this number is insufficient and doubts the random distribution of gift vouchers in the different stores of the chain.\\
Are his doubts justified?