Answer Happy

Error-correcting codes¹ are used in order to compensate for errors in transmission of messages (and in recovery of stored data from unreliable hardware). You are on a mission to Mars and need to send regular updates to mission control. Most of the packets actually don't get through, but you are using an error-correcting code that can let mission control recover the original message you send so as long as at least 1024 packets are received (not erased). Suppose that each packet gets erased independently with probability 0.7. How many packets should you send such that you can recover the message with probability at least 99% Use the Central Limit Theorem to approximate the answer, using the continuity correction. Your answers should be correct to 4 decimal places.