The heights of 16-month-old oak seedlings are normally distributed with a mean of 31.5 cm and a standard deviation of 10 cm. What is the range of heights between which 5 % of the seedlings will grow? (Please also explain and show how you got your z-score)

I did:

5% = 95% - 90%

Z - Score *Found using the z - score table*:

95% = 1.64 and 90% = -1.64

31.5 + 1.64(10) and 31.5 - 1.64(10)

47.9 and 15.1 cm

Am i right?