One of your friends is testing the effect of drinking coffee on the duration of cold symptoms. the common cold lasts, on average, 6 days. she starts with no expectations as to whether drinking coffee will have any effect at all on cold duration. after seeing the results of her experiment, in which the average cold duration was less than 6 days, she tests a one-sided alternative about the population mean cold duration when drinking coffee,

h0: μcoffee = 6

ha: μcoffee < 6

she finds z = −1.68 with one-sided p-value p = 0.0465.

what is the correct two-sided p-value for z = −1.68? round your answer to 4 decimal places.